Hi, perseph! There are literally thousands of asteroids, each one (as it is discovered) assigned a name and/or number -- it would be impossible to utilize each one in horoscopes, so many astrologers prefer to focus the influence of the asteroid belt through a basic four: Pallas Athena, Vesta, Ceres and Juno.
Asteroids seem to modify planetary energy in very specific ways (much as tarot card meanings can be amplified by additional draws), and some people have speculated that their influence is fateful. Theories abound. A good introductory book on the subject is Asteroid Goddesses by Demetra George.
If you are just beginning your astrological studies, my suggestion would be to establish a solid foundation of understanding by working with planets, signs, houses and aspects; initially, the addition of extraplanetary influences can clouds issues, instead of clarifying them.
Many experienced astrologers prefer not to use asteroids at all, and others swear by them. This is yet another area in which one needs to keep an open mind, and experiment with many charts.