With a new deck, the first time I shuffle it I will lay all the cards face down on the table and mix them around thoroughly. It does not matter to me if some cards get turned upside down in the process. Then, I re-assemble the deck (keeping all the cards face down). Then, holding the deck in one hand (either my left or right), I pull some cards out of the deck with my other hand, then sift them to the front and back of the deck. And I repeat this process of sifting cards from hand to hand, putting them back in different places in the deck, until I feel satisified that the deck is well mixed. It make take only a few minutes, or it may take 10 minutes...it just varies.
After I've used a deck a few times and know that the cards are sufficiently randomized already, then I don't always lay them down and mix them first (sometimes I will, if I feel like it, but not always). Often, I'll just go through the process of sifting cards (I don't know, but I think some people call this hand over hand shuffling) for a few minutes. By the way, I never put a deck back in order unless I'm planning to study it.
I do not deliberately turn or flip cards in order to achieve reversals. When I lay out the spread, some cards will turn up reversed, but if they do, I just turn them back around upright.
Questions of which way to turn the cards, or whether or not the querent shuffles the deck do not come up for me, as I am not doing face-to-face readings right now...I'm only reading online, with a few exceptions. But generally speaking, if it ever came up, I would not let the querent shuffle. I would, however, allow them to pick the cards up to examine them during the reading, or to look through the deck after the reading if they were curious.
I never riffle shuffle. Tried it once...and creased a card. Felt sick about it for days. And so I don't riffle shuffle anymore.
My reasoning for how I shuffle and handle the cards is simply that it works for me...and it is gentle on the cards. Keeping my cards in good condition is important to me. Keep in mind that I'm not a professional reader, and I'm not out there reading for live querents...so right now, having a "well-worn" deck for purposes of looking like I know what I'm doing does not matter to me.
I do not have any special or spiritual rituals that I follow when shuffling a deck. I do usually cut the deck before drawing the cards, but I do not pay attention to which hand I am using to hold and cut the deck, nor do I have a certain number of times that I always cut it. Nor do I care which pile goes back on top, or which pile I draw from. Sometimes I draw cards straight off the top, in order. Other times I draw randomly from the deck. I just do whatever strikes me at the moment.