what is the process?
Finding dogs who are excellent representations of the breed that have clean genetic lines. The point of breeding is to improve the breed - to have the puppies be standard conformation and also weed out genetic defects common to Yorkies
do you have to registered all your dogs with AKC, etc?
AKC is the most reputable organization. You can't just register any dog w/ the AKC; their parents need to be registered and their litter's registration needs to be sent in by the breeder.
do you need a license?
Not usually.
You probably shouldn't breed any dogs that you got at pet stores. You don't know their historys or what their parents looked like or anything else. Dogs from pet stores are usually from puppymills. Check out this site:
http://www.stoppuppymills.org/