One of the most exciting discoveries of sign language research is that children acquiring sign languages go through the same linguistic stages that those acquiring spoken languages do. First they babble, experimenting with the basic units of the language (sounds in the case of spoken language and handshapes, movements, and locations in the case of sign). Then they begin to structure the babbling into words, making cute mistakes along the way, before ultimately gaining control over word production.
This video from Handspeak shows how nine specific signs (plus some fingerspelled words) are acquired by one child from 6 months to 3 years old. For the first sign "work," for example, she moves from the general hand movement, to the proper handshape, to the proper handshape and relationship between the two hands. It's a fascinating look at the natural blossoming of language over time.