Take a bill of sale to the County Clerk's Office (same place you get your car tags) and begin the registration process. If the previous owner gave you his registration card (they seem to always do that) give it back to him. It says on the back that he has 15 days to mail it to the Boating Division and say he has sold the boat.
If you keep the boat and need to renew the registration, you can go to any license agent to do the renewal.