My ds used to move around a lot in the crib.
Last spring we got rid of the sleeping bag and introduced the blanket. Since it was warm, getting out of the covers wasn't a problem. When the colder weather started hitting, we noticed that ds started staying under the covers and reaching to get them.
I put a pillow in the crib last summer or so. For the first several months he was totaly ignoring it, sleeping below it, then he started sleeping on it on his own (that's about when the crib travelling stopped).
Finally we took the side off the crib and he got a "big boy bed" several weeks ago. Since nothing else changed, he took it really well.
So, it took a while, but it was very easy.