I coslept with our dd for the first 4 months and the only way that I was able to move her into her own bed was by doing a bedtime routine. I started this at 3 months old and then moved her at 4 months. By the time she moved to her bed she knew that the bedtime routine (bath, nurse and read 2 books) meant that she was out for the night. She is settled now and I can just lay her in her crib and she will put herself to sleep.
How I transitioned her to her crib from our bed:
For the first week or 2 I would do the bedtime routine (the exact same thing every night) and then pat/shhh her in her crib until asleep. If she woke up before 1am, I would pat/shh her again or if hungry would feed her. If she woke up after 1am, I would bring her to our bed. After about 2 weeks of this, if she woke up after 1am, I would feed her and then put her back into her bed. It only took about 2 days for her to be comfortable in her crib the whole night!
Also, I think it is a great idea to let them play in their crib, it makes them feel safe once they are left in there!
Good luck and if you have any other questions, PM me anytime!