It goes something like this:
The buyer verifies that his FFL will accept a gun from a non FFL (you).
The buyer has his FFL mail you a copy of their license (FFL).
The buyer mails you payment (I would insist on a USPS MO).
After you receive payment and the FFL, you ship the gun and a copy of your driver's license directly to the FFL.
Now shipping a handgun by a non FFL is tricky and expensive - figure about $50. There are specific rules about how and what kind of shipping a non-FFL must use when shipping a handgun. If you have a local FFL you have a relationship with, I suggest letting them ship the handgun. Less hassle, they can ship cheaper than a non FFL, charge you a fee for their service, and it should still run about $50 (or less).