Some states allow sales within state from user to user, but assuming a legal transfer of ownership everywhere:
#1 have the BUYER send you a copy of the dealer FFL(license) he chooses to receive the rifle and complete the transfer from your name to his.
To speed this up, you can just get the FFL and phone numbers from the buyer for his recieving dealer. Then check that it's a valid license here:
#2 Call the dealer to be sure he has a heads up that it's coming just before shipping & remind him who it's for.
#3 Have the buyer let you know when he has it, and verify with the dealer that the transfer took place. He can then send you a copy of his license for your records.
It's really a good idea to keep all transaction & shipping records -forever. If the transfer didn't occur(you'll never really know), and the gun is someday found at a crime scene, the heat will be knocking on your door(they may knock it down). It's peace of mind.
As for shipping....depends on your area. The post office, UPS, just be sure to go to their websites and research packing and shipping instructions for firearms. It may take some patience, as most shippers know less about firearm shipping than you by then. You'll likely have to gently educate them.
Do not commit to sending ammo. It ain't worth it, trust me!