Wikipedia
Wikipedia lists many "common" methods of divination:
abacomancy /ˈæbəkɵmænsi/: by dust (Hebrew ’ābāq, dust + Greek manteia, prophecy)
acultomancy /əˈkʌltɵmænsi/ (also acutomancy): by needles (from acutomancy below, influenced by Latin acūleus, needle)
acutomancy /əˈkjuːtɵmænsi/ → see acultomancy above (Latin acus [acut-], needle + Greek manteia, prophecy)
adromancy /ˈædrɵmænsi/ → see alomancy below (from idromancy below, influenced by alomancy)
adryomancy→ see hydromancy below (metathesis of hydromancy)
aeromancy /ˈɛərɵmænsi/: by atmospheric conditions (Greek āēr, air + manteia, prophecy)
agalmatomancy /əˈɡɔːlmətɵmænsi/:[citation needed] by statues (Greek agalma [agalmat-], statue + manteia, prophecy)
aichmomancy /ˈɛkmɵmænsi/: by sharp objects (Greek aikhmē, spearhead + manteia, prophecy)
ailuromancy/aeluromancy → see under theriomancy below
alectormancy/alectromancy /əˈlɛktrɵmænsi/: by rooster sacrifice (Greek alektor, rooster + manteia, prophecy)
alectryomancy/alectoromancy → see under theriomancy below
aleuromancy¹ /əˈljʊərɵmænsi/: by flour; see also under chartomancy below (Greek aleuron, meal + manteia, prophecy)
alomancy/Halomancy /ˈælɵmænsi/ (also adromancy): by salt (Greek hals, salt + manteia, prophecy)
alphitomancy /ˈælfɨtɵmænsi/: by barley (Greek alphis [alphit-], barley + manteia, prophecy)
alveromancy /ælˈvɪərɵmænsi/:[citation needed] by sounds
amathomancy /ˈæməθɵmænsi/: by sand (Greek amathos, sandy soil + manteia, prophecy)
ambulomancy /ˈæmbjʊlɵmænsi/: by walking (Latin ambulāre, to walk + Greek manteia, prophecy)
amniomancy /ˈæmni.ɵmænsi/: by placenta (Greek amniōn, amnion + manteia, prophecy)
anemoscopy/anemomancy /ˌænɨˈmɒskɵpi/: by wind (Greek anemos, wind + -skopiā, observation)
anthomancy /ˈænθɵmænsi/: by flowers (Greek anthos, flower + manteia, prophecy)
anthropomancy /ænˈθrɒpɵmænsi/: by human sacrifice (Greek anthrōpos, human being + manteia, prophecy)
anthroposcopy /ænθrɵˈpɒskɵpi/: by physical appearance (Greek anthrōpos, human being + -skopiā, observation)
anthracomancy /ˈænθrəkɵmænsi/: by burning coals (Greek anthrax [anthrak-], charcoal + manteia, prophecy)
apantomancy /əˈpæntɵmænsi/: by chance encounters with animals (Greek apantein, to encounter + manteia, prophecy)
arachnomancy /əˈræknɵmænsi/: by spiders (Greek arakhnē, spider + manteia, prophecy)
archeomancy/archaeomancy /ˈɑrki.ɵmænsi/: by sacred relics (Greek arkhaios, ancient + manteia, prophecy)
arithmancy/arithmomancy/arithmosophy /ˈærɨθmænsi, əˈrɪθmənsi/ [1]: by numbers (Greek arithmos, number + manteia, prophecy)
ariolation /ˌæriɵˈleɪʃən/: by altars (Latin ariolus, hariolus, prophet)
armomancy /ˈɑrmɵmænsi/: by one's own shoulders (Latin armus, shoulder + Greek manteia, prophecy)
aruspicina: study of entrails [2]
aspidomancy /ˈæspɨdɵmænsi/: by sitting in a drawn circle (Greek aspis [aspid-], shield + manteia, prophecy)
astragalomancy/astragalamancy → see under cleromancy below
astragyromancy → see under cleromancy below (from astragalomancy above, perhaps influenced by Greek guros, spiral, circle, and therefore vertebra)
astrapomancy /ˈæstrəpɵmænsi/: by lightning (Greek astrapē, lightning flash + manteia, prophecy)
astrology/astromancy/astroscopy /əˈstrɒlɵʤi/: by celestial bodies (Greek astron, star + -logiā, study)
augury /ˈɔːɡjʊri/ → see under theriomancy below
auramancy /ˈɔːrəmænsi/: by auras (Greek aurā, breath + manteia, prophecy)
auspicy/auspication → see under theriomancy below (Latin avis, bird + specere, to look at)
austromancy → see under theriomancy below, /ˈɔːstrɵmænsi/: by wind (Latin auster, south wind + Greek manteia, prophecy)
avimancy → see orniscopy below (Latin avis, bird + Greek manteia, prophecy)
axiomancy/axinomancy /ˈæksi.ɵmænsi/: by axes (Latin axis, axis + manteia, prophecy)
batraquomancy/batrachomancy /bəˈtrækɵmænsi/: by frogs (Greek batrakhos, frog + manteia, prophecy)
belomancy/bolomancy /ˈbɛlɵmænsi/: by arrows (from bolomancy below, influenced by Greek belemnon, javelin, or belonē, needle)
bibliomancy → see chartomancy below
biorhythmic divination: by biorhythms
bletonism/bletonomancy /ˈblɛtənɪzm/: by water current (named for Monsieur Bleton, a French bletonist)
bolomancy /ˈbɒlɵmænsi/ → see belomancy above (Greek bolē, arrow + manteia, prophecy)
botanomancy /bɵˈtænɵmænsi/: by burning sage or figs (Greek botanē, flora + manteia, prophecy)
brizomancy → see oneiromancy below (Greek brizein, to be sleepy + manteia, prophecy)
brontomancy/brontoscopy /ˈbrɒntɵmænsi/: by thunder (Greek brontē, thunder + manteia, prophecy)
bumpology /bʌmˈpɒlɵʤi/: by bumps on the skin (English bump + Greek -logiā, study)
canomancy /ˈkænɵmænsi/ or /ˈkeɪnɵmænsi/: by dogs (Latin canis, dog + Greek manteia, prophecy)
capnomancy /ˈkæpnɵmænsi/: by smoke (Greek kapnos, smoke + manteia, prophecy)
carromancy /ˈkærɵmænsi/: by melting wax (Greek karrō, of wax + manteia, prophecy)
cartopedy → see under somatomancy below (Latin carta, papyrus paper + pēs [pēd-], foot)
cartomancy → see under chartomancy below
catoptromancy/captromancy → see under scrying below
causimancy/causimomancy /ˈkɔːzɨmænsi/: by burning (Greek kaiein [kaus-], to burn + manteia, prophecy)
cineromancy/ceneromancy /ˈsɪnərɵˌmænsi/: by ashes (Latin cinis [ciner-], ashes + Greek manteia, prophecy)
cephalomancy → see under somatomancy below
cephaleonomancy/cephalonomancy/ˌsɛfəliˈɒnɵmænsi/: by boiling a donkey's head (Greek kephalaion, head [with meaning influenced by Greek onos, donkey] + manteia, prophecy)
ceraunoscopy /ˌsɛrəˈnɒskɵpi/: by thunder and lightning (Greek keraunos, thunderbolt + -skopiā, observation)
ceromancy/ceroscopy /ˈsɛrɵmænsi/: by dripping wax in water (Greek kēros, wax + manteia, prophecy)
chalcomancy: by striking gongs or copper bowls (Greek khalkos, copper + manteia, prophecy)
chaomancy /ˈkeɪ.ɵmænsi/: by aerial visions (Greek khaos, primordial space + manteia, prophecy)
chartomancy /ˈkɑrtɵmænsi/: by things on paper (Greek khartēs, papyrus paper + manteia, prophecy)
cartomancy /ˈkɑrtɵmænsi/: by cards (Latin carta, papyrus paper + Greek manteia, prophecy)
taromancy/tarotmancy /ˈtærɵmænsi/: by tarot (English tarot + Greek manteia, prophecy)
stichomancy /ˈstɪkɵmænsi/: by books or lines (Greek stikhos, line of verse + manteia, prophecy)
aleuromancy² /əˈljʊərɵmænsi/: by fortune cookies (of the same origin as aleuromancy¹ above)
bibliomancy /ˈbɪbliɵmænsi/: by the Bible (Greek biblion, book + manteia, prophecy)
I Ching divination: by the I Ching or the accompanying I Ching manual
stoicheomancy/stoichomancy: by the Iliad and the Odyssey or the Aeneid (Greek stoikheion, element + manteia, prophecy; to the Greeks, Homer's writings were held in similar esteem to the Christian Bible or the Muslim Quran, as were Virgil's writings to the Romans, making them the basic — or elementary — reading material in each culture)
cheiromancy/chiromancy→ see under somatomancy below
cheirognomy/chirognomy → see under somatomancy below
chien tung → see kau cim below
choriomancy /ˈkɒri.ɵmænsi/: by pig bladders (Greek khorion, placenta + mantiea, prophecy)
chresmomancy /ˈkrɛsmɵmænsi/: by the ravings of lunatics (Greek khrēsmos, oracular utterance, chresm + manteia, prophecy)
chronomancy /ˈkrɒnɵmænsi/: by apt occasion (Greek khronos, time + manteia, prophecy)
clamancy (see also Fāl-gūsh): by random shouts and cries heard in crowds, at night, etc. (Latin clāmāre, to cry out + Greek manteia, prophecy)
cledonism/cledonomancy /ˈklɛdɵnɪzm/: by chance events or overheard words (Greek klēdon, rumor)
cleidomancy/clidomancy /ˈklaɪdɵmænsi/: by keys (Greek kleis [kleid-], key + manteia, prophecy)
cleromancy /ˈklɛrɵmænsi/: by casting (Greek klēros, lot + manteia, prophecy)
astragalomancy/astragalamancy /əˈstræɡəlɵmænsi/ (also cubomancy): by dice (Greek astragalos, vertebra + manteia, prophecy)
domino divination: by dominoes
favomancy /ˈfævɵmænsi/: by beans (Latin faba, bean + Greek manteia, prophecy)
Ogham casting: by Ogham letters
runecasting/Runic divination: by runes
cometomancy /kɵˈmɛtɵmænsi/: by comet tails (Greek komētēs, comet + manteia, prophecy)
colormancy/coloromancy: by colors (English color + Greek manteia, prophecy)
conchomancy /ˈkɒŋkɵmænsi/: by shells (Greek konkhē, mussel + manteia, prophecy)
cosquinomancy/coscinomancy /kɵˈsɪnɵmænsi/: by hanging sieves (Greek koskinōn, sieve + manteia, prophecy)
cottabomancy/cottobomancy /ˈkɒtəbɵmænsi/: by wine in a brass bowl (Greek kottabos, cottabus + manteia, prophecy)
craniognomy /ˌkreɪniˈɒɡnɵmi/ or /ˌkreɪniˈɒnəmi/ → see under somatomancy below (Greek krānion, skull + -gnōmoniā, interpretation)
the crawling baby: by a baby's crawling
crithomancy/critomancy /ˈkrɪθɵmænsi/: by barley cakes (Greek krithē, barley + manteia, prophecy)
cromnyomancy/cromniomancy /ˈkrɒmni.ɵmænsi/: by onion sprouts (alteration of Greek krommuon, onion + manteia, prophecy)
cryptomancy /ˈkrɪptɵmænsi/: by omens (Greek kruptos, hidden + manteia, prophecy)
crystal ball gazing → see under scrying below
crystal gazing → see under scrying below
crystallomancy /ˈkrɪstəlɵmænsi/ → see under scrying below (Greek krustallos, crystal + manteia, prophecy)
cubomancy /ˈkjuːbɵmænsi/ → see under cleromancy above (Greek kubos, cube + manteia, prophecy)
cyathomancy /ˈsaɪ.əθɵmænsi/: by cups (Greek kuathos, cup + manteia, prophecy)
cybermancy /ˈsaɪbərmænsi/: by computer oracles (English cyber(netics) + Greek manteia, prophecy)
cyclicomancy /ˈsɪklɨkɵmænsi/: by swirling water in a cup (Greek kuklikos, cyclical, circular + manteia, prophecy)
cyclomancy /ˈsɪklɵmænsi/ or /ˈsaɪklɵmænsi/: by wheels (Greek kuklos, circle + manteia, prophecy)
dactyliomancy /dækˈtɪliɵmænsi/: by finger rings (Greek daktulios, finger ring + manteia, prophecy)
dactylomancy /ˈdæktɨlɵmænsi/ : by means of finger movements (Greek daktulos, finger + manteia, prophecy)
daphnomancy /ˈdæfnɵmænsi/: by burning laurel wreaths (Greek daphnē, laurel + manteia, prophecy)
demonomancy /dɨˈmɒnɵmænsi/: by demons (Greek daimōn, divine power + manteia, prophecy)
dendromancy /ˈdɛndrɵmænsi/: by trees, especially oaks, yews, or mistletoe (Greek dendron, tree + manteia, prophecy)
deuteroscopy /ˌdjuːtəˈrɒskɵpi/: by second glance or double take (Greek deuteros, secondary + -skopiā, observation)
dictiomancy /ˈdɪkʃɵmænsi/: by randomly opening a dictionary (English dictio(nary) + Greek manteia, prophecy)
divining → see dowsing below
djubed → see under scrying below
dōbutsu uranai: by animal horoscope (Japanese dōbutsu, animal + uranai, prognostication)
domino divination → see under cleromancy above
dowsing (also divining, water witching): by a divining rod (of unknown origin)
dracomancy /ˈdrækɵmænsi/: by dragons (Greek drakōn, dragon + manteia, prophecy)
dream questions: by dreaming
dririmancy/driromancy /ˈdrɪərɨmænsi/: by dripping blood (alteration of drimimancy, influenced by Middle English drir, blood)
drimimancy/drymimancy /ˈdrɪmɨmænsi/: by bodily fluids (Greek drimus, pungent + manteia, prophecy)
eleomancy/elaeomancy: by oil (Greek elaion, olive oil + manteia, prophecy)
emonomancy → see demonomancy above[citation needed]
empyromancy /ɛmˈpaɪrɵmænsi/: by burning (Greek empurios, fiery + manteia, prophecy)
enochian chess: by playing a four·handed variant of the game
enoptromancy /ɛˈnɒptrɵmænsi/ → see under scrying below (Greek enoptron, looking glass + manteia, prophecy)
enthusiasm: speeches by those supposed to be possessed by a divine spirit
entomomancy/entomancy: by insects (Greek entomon, insect + manteia, prophecy)
eromancy /ˈɛrɵmænsi/: by water vessels exposed to air (Greek āēr, air + manteia, prophecy) — cf. aeromancy
extispicy/extispication /ɛkˈstɪspɨsi/: by the remains of sacrificed animals (Latin exta, entrails + specere, to look at)
favomancy → see under cleromancy above
felidomancy → see under theriomancy below (Latin fēlēs [fēlid-], cat + Greek manteia, prophecy)
feng shui → see under geomancy below
floriography/floromancy /ˌflɔriˈɒɡrəfi/: by flowers' feelings (Latin flōs [flōr-], flower + Greek -graphiā, representation)
fractomancy /ˈfræktɵmænsi/: by fractals (English fract(al) + Greek manteia, prophecy)
fructomancy/fructimancy: by fruit (Latin frūctus, fruit + Greek manteia, prophecy)
galvanoscopy /ˌɡælvəˈnɒskɵpi/: by galvanism (English galvan(ism) + Greek -skopiā, observation)
gastromancy¹ → see under scrying below
gastromancy² /ˈɡæstrɵmænsi/: by guttural sounds (Greek gastēr, belly + manteia, prophecy)
geomancy /ˈʤiːɵmænsi/: by earth (Greek Gaia|gē, earth + manteia, prophecy)
feng Shui divination: by Feng Shui
geloscopy /ʤɨˈlɒskɵpi/: by laughter (Greek gelōs, laughter + -skopiā, observation)
gematria: by the Hebrew alphabet (Greek gē, earth + -metriā, measurement)
genethlialogy: by birth dates (Greek genethlios, birthday + -logiā, study)
grammomancy /ˈɡræmɵmænsi/: by writing individual letters (Greek gramma, letter + manteia, prophecy)
graphology /ɡræˈfɒlɵʤi/ (also graptomancy): by studying handwriting (Greek graphē, writing + -logiā, study)
graptomancy /ˈɡræptɵmænsi/ → see graphology above (Greek graptos, written + manteia, prophecy)
gyromancy /ˈʤaɪrɵmænsi/: by dizziness (Greek gūros, spiral + manteia, prophecy)
hagiomancy: by saints (Greek hagios, holy + manteia, prophecy)
halomancy /ˈhælɵmænsi/ → see alomancy above.
hakata: by bones or dice
haruspicy/haruspication /həˈrʌspɨsi/ → see hepatoscopy below (Latin haru-, entrails + specere, to look at)
hematomancy/haematomancy /ˈhɛmətɵmænsi/ or /ˈhiːmətɵmænsi/: by blood (Greek haima [haimat-], blood + manteia, prophecy)
hepatoscopy/hepatomancy /ˈhɛpətɵmænsi/ (also haruspicy, haruspication): by liver (Greek hēpar [hēpat-], liver + -skopiā, observation)
hieromancy/hieroscopy /ˈhaɪrɵmænsi/ or /ˈhaɪərɵmænsi/: by studying sacrifices' entrails (Greek hieros, holy + manteia, prophecy)
hippomancy → see under theriomancy below.
horoscopy /hɵˈrɒskɵpi/: aspect of the Stars at nativity [4] (Greek hōrā, season + -skopiā, observation)
hydatomancy: by rainwater (Greek hudatis, raindrop + manteia, prophecy)
hydromancy/hydroscopy → see under scrying below
hyomancy: by wild hogs (Greek hūs, swine + manteia, prophecy)
hypnomancy /ˈhɪpnɵmænsi/: by sleep (Greek hupnos, sleep + manteia, prophecy)
I Ching divination → see under chartomancy above.
ichnomancy /ˈɪknɵmænsi/: by footprints (Greek ikhnos, track + manteia, prophecy)
ichthyomancy → see under theriomancy below
iconomancy /aɪˈkɒnɵmænsi/: by icons (Greek eikōn, image + manteia, prophecy)
idolomancy /aɪˈdɒlɵmænsi/: by idols (Greek eidōlon, phantom + manteia, prophecy)
idromancy → see alomancy above (Greek idrōs, sweat + manteia, prophecy)
ifá: by palm nuts
iridology: by eye color (Greek īris [īrid-], iris + -logiā, study)
isopsephy: by numbers and letters (Greek īsos, equal + psephos, pebble)
Jyotish: Vedic system of astrology
kabbalah/qabalah/cabala: by the Kabbalah (Hebrew qabbālâ, tradition)
kau cim: by bamboo
kephalonomancy /kəˈfælənɵmænsi/ → see cephaleonomancy above
keraunomancy /kɨˈrɒnɵmænsi/ → see ceraunoscopy above
knissomancy /ˈnɪsɵmænsi/: by incense (Greek knisa [kniss-], vapor + manteia, prophecy)
kypomancy → see under phyllomancy below (akin to Greek kupellon, goblet + manteia, prophecy)
labiomancy /ˈleɪbi.ɵmænsi/: by lips (Latin labium, lip + Greek manteia, prophecy)
lampadomancy /ˈlæmpədɵmænsi/: by flame (Greek lampas [lampad-], light + manteia, prophecy)
lecanomancy/lecanoscopy /lɨˈkænɵmænsi/: by a basin of water (Greek lekanē, basin + manteia, prophecy)
letnomancy: by secrets (English let no (one see) + Greek manteia, prophecy)
libanomancy /laɪˈbænɵmænsi/: by smoke from incense (Greek libanos, frankincense + manteia, prophecy)
literomancy /ˈlɪtərɵmænsi/: by a letter in a written language (Latin lītera, letter + Greek manteia, prophecy)
lithomancy /ˈlɪθɵmænsi/: by precious stones (Greek lithos, stone + manteia, prophecy)
logarithmancy /ˌlɒɡəˈrɪθmənsi/: by logarithms (English logarith(m) + Greek manteia, prophecy)
logomancy /ˈlɒɡɵmænsi/: by words (Greek logos, word + manteia, prophecy)
lots: divination through chance, or the drawing or tossing of lots[5]
lunamancy → see selenomancy below (Latin lūna, moon + Greek manteia, prophecy)
lychnomancy /ˈlɪknɵmænsi/: by candles (Greek lukhnos, lamp + manteia, prophecy)