1. Contact the buyer. Tell him you want a copy of his receiving FFL's license either faxed or e-mailed to you. Don't sweat the IA Pistol Permit. He shows that to his FFL at the time of the NICS check to get the gun, not to you.
2. When you get it, go to the ATF's FFL eZCheck
here, and make sure the FFL is still valid.
3. Have the buyer contact his FFL and ensure his FFL will accept shipment from a "non-licensee" (that's you). Some FFL's won't.
4. Prepare a letter for the FFL explaining who the gun is going to, along with all his contact info, and stick it in an envelope. That way the gun doesn't just "show up," and the FFL is left thinking, "Who the hell is this for?" Include your contact info, too, so the FFL can write something in his book. I include a copy of my DL, but that's optional.
5. I like to make out two copies of a bill of sale, sign both, and include one with a SASE and ask the buyer to send a signed copy back, but that's optional.
6. Package and ship the gun (and paperwork above) via either UPS or FedEx to the business address on the FFL's license. Have it boxed before you go to the shipping center. (I have online accounts with both shippers, and fill out my labels at home, too. I just hand the box to the folks behind the counter, good to go.) Both UPS and FedEx have policies requiring you to send them Overnight.
7. E-mail the tracking number to the buyer.
Any other questions, just ask.