Unless its sold to a resident of your state, a handgun can only be shipped to an FFL. No exceptions. (FFLs can shipt to other FFLs using the US Postal Service, non-licensee can't.)
You can have an FFL/dealer ship it for you, or you can ship it to an FFL, yourself.
Either way, ask the seller to send you an ink-signed copy of his license along with payment. The ATF now says that faxed copies of the FFL are acceptable, so he could technically send you a copy by email. (Then, if its not an ink-signed copy, you can go to the ATF website and verifiy that its a valid license.)
Once you've received the FFL and cash/payment, you package the gun up and go to FedEx or UPS and ship it.
The ATF regs say you must use a common carrier. The only two common carriers who will do it are FedEx and UPS. Both charge a premium for shipping handguns. A big premium (as much as $50+).
The ATF regulations say you MUST tell the carrier are shipping a weapon (in writing, but few do that.)
Others here have advocated calling the gun machine parts and just shipping it to the FFL. I won't do that. As far as I can tell that's not right, not ethical, but probably not illegal (except you haven't declared the weapon to the carrier, as required by the regs.)
The receiving FFL will take care of the transfer details for the state in which its received and see that the buyer gets the gun legally. The buyer will pay the FFL for his work.
Let us know what you'll take in trade (in the General Firearms-Classified area.) I may have something you'll like.