My daughter was 27 months when we moved her to a "big girl bed" We skipped the toddler bed. She wasn't climbing out of her crib and was completely happy with it and probably would have stayed until she was 5! We moved her because we needed the crib for baby2 who is due in Feb. I didn't want to take the crib away and immediately give it to the new baby. I wanted her to forget it...
This is what worked for us: Put one side of the bed up against the wall. It will give her a sense of security since that is probably how the crib was set up. We tried only having her head up against the wall -- BIG mistake. she just kept getting out.... Once we moved the bed so one side was against the wall she was obviously happier. We also let her take ALL of her favorite stuffed animals to bed and would line them up on the outside of the bed. I think this helped her to feel more secure.
The other thing, when Lily would get up, we would walk her back to bed, tuck her in and leave with as little interaction as possible. Eventually, since she got no interaction from us, she got bored and just stay in bed. It took about a week for my daughter to get it. It does help though that we close her door when we leave. We will also let her take a book to bed so she can "read". She doesn't have a night light so she will pretend.
Don't get mad when she gets up and be prepared to possibly sleep in there with her, or until she falls asleep or to wake up and find her in your bed. It is a process and, like teaching her to sleep through the night, you do have to teach her to sleep in her bed. Have patience. Good Luck!