Many amputees can still move the muscles/surface at end of their limb. So they put a sensor and then try to make an intuitive map of those skin/muscle movements to the bionic arm motions. I don't know how exactly they map the motions (statically vs a learning algorithm, etc), but apparently they can make it good enough that people can learn how to use the bionic arm naturally.
(Forgot exactly where I saw this. Hopefully someone can provide a source.)
EDIT: Looks like recently they've been able to actually rewire nerves. Short video here:
http://www.newscientist.com/blogs/nstv/2011/02/bionic-arm-wi...