It's difficult to say how long it took because it's sort of a gradual process, and I'll still sleep on my stomach on the rare occasion. I think it probably took a couple weeks to get used to it and a month to really prefer it. As far as sleeplessness, it wasn't too bad. At first I'd have a little more difficulty falling asleep and be tempted to just turn over, but I got past that fairly quickly. I'd also wake up every now and then but it honestly wasn't that bad.
I'd been sleeping on my stomach for a long time so when my chiropractor told me to switch, I really didn't think I'd be able to do it. I'd suggest at least trying it for a few weeks to see how it goes.