Hi T.,
Great question! I wondered that for a long time myself. We only recently made the switch, one week before our daughter turned 3 years old. She never tried to climb out of her crib (thankfully) and enjoyed sleeping there so we were in no hurry to push her into a needless change.
Before we converted her bed, we talked about it for some time (a few weeks) beforehand, off and on, gauging her reaction. Before long she became excited about it and that let us know it was getting to be time. We would have tried it a bit sooner than we did (maybe a week or so sooner), but what we did was convert our crib to a toddler bed (it's one that is made to do that) and I needed my husband's mechanically-skilled help to do it.
Rachel was VERY EXCITED that day and very happy to have a "big girl bed!" We put a big pillow on the floor next to it when she went to bed (my husband still insists on doing this for now) and the first night she sort of crawled out onto it one time and was hunkered down on it, still asleep. I think this happened because she always tended to press herself against the outer side of the crib (not the wall facing side) and when the side was gone, she had to get used to that. She has rolled out one time since, but it didn't even wake her up, we just heard the little thump and went and put her back into bed. :) She seems to have adjusted well and still occasionally makes a happy comment about having a "big girl bed!" :)
One more thing - she still doesn't sleep with a pillow as yet. I've offered a small one a few times, but she only wants to play with it (pretend night-night for her or one of her bears etc.), not actually sleep with it. Our chiropractor didn't encourage pillow usage, and said if/when she decided she wanted one, to keep it small and as flat as possible, not big and puffy.
GOOD LUCK - I hope it will be a very happy time for your daughter as it was for ours...it's a real milestone!
S.