I was really nervous about this transition, mainly because I worked so hard getting DD to fall asleep independently and she did this no problem in the crib. I was so worried that moving her to a bed would be starting all over again. We have had the "big girl" bed in her room from Day One (we knew we'd have two kids while we lived in this apartment, so set up the room that way, with DH's old bed from when he was a kid). She would play on it, and very occasionally, when she was sick, we would co-sleep with her in it when she couldn't get to sleep any other way. But up until we made the transition, she would just play on it and that was it-- she didn't really see it as a place to sleep. So we started talking to her about how she would move to the big-girl bed, and she'd sleep there for naps and at night. DH then asked her at just over two years old (about 24.5 months) if she wanted to sleep in her bed for nap and she said yes. So we tried it out for nap. It took a bit longer for her to fall asleep, but she did, and we actually had to wake her up from that nap. She asked to sleep in it that night, but I didn't feel ready for it, so she went back into the crib. The next day she napped great in the big-girl bed again, and when she asked that night to sleep in it, we let her. We haven't looked back. It took her about 3 weeks to realize that she could get out of it, and when she did, we had a couple days of no naps, but then she was back on track.
Honestly, I was more worried about this transition than I was about potty training (which is why it was good that DH took the initiative to start working on this), but it went so much more smoothly than I could have imagined.