It's easy. If the
boat is small it's likely state registered with the DMV. Take the title in and they'll transfer it into your name and give you
current registration for a small fee. You'll have to pay sales tax (at least that's the case here in Cali).
If on the other hand the boat is Documented, you will not be able to have new
documentation issued in your name, as you must be a US citizen. If this is the case you need to have the old owner contact the
documentation center and tell them the boat has been
sold, and then you need to call and have the boat " removed " since you will be state registering. In Cali you do not need proof of this (by way of a letter the doc center can send you for a fee) - other states may require the letter. Once this is done you go to the DMV and they will get you a state issued title and new
registration #'s.
USCG National Vessel Documentation Center, Home Page