C.R.
My daughter transitioned to a big girl bed when she was 21 months. At first, she didn't even realize she could climb out! We got her a twin bed and put bed rails on it so she couldn't fall out. Once she started to get out of bed we used Super Nanny's technique - don't laugh cause it worked like a charm. Here's what we did:
Bath, brush teeth, book, hugs, kisses, bed. The first time she got out of bed we'd put her back in bed and say "Goodnight" and give kisses & hugs again. The second time she got out of bed we'd put her back in bed and only say "goodnight", no hugs and kisses this time. The third and additional times we'd put her back in bed and say nothing, no hugs, no kisses.
The first night took the longest, probably 10 times out of bed if not more. The second night was about 1/2 as much, the third night was only a time or two out of bed. By then, she'd stay in.
Good luck!!