Here's a link to the ATF site. I recommend sending them to a FFL since they'll be well versed on receiving firearms through the mail and as a business will accept packages instead of them sitting on your parents' front doorstep with nobody home. They may charge a fee though to accept them and hand them over to the owners.
Parents settle in and find a FFL that is willing to accept the Transfers. Its good to provide a list of what is being shipped and when. That FFL should provide a copy of his FFL and EXACT Ship to Address and Phone # and email address. Good email communication is great but stick to necessities, don't pester with requests for constant updates.
A Copy of the FFL Doc should be placed in each Package along with a Copy (both sides) of your drivers license, and another typed page with Who's shipping /address/phone (you), who's receiving/address/phone (FFL), for further transfer to Parentsname/address/phone and discription of firearm(s) in pkg: Colt SporterII, AR15A2 semiautomatic rifle, 20 inch barrel Ser# 1234567 with 3× Colt Scope, mag or no mag. Parents will pay a Transfer fee on each firearm to the receiving FFL and a Standard NICS or State background check with each seperate pickup but several firearms can go on one NICS Form.
Have another Copy of all three documents in hand when you go to the Selected Shipper so they can see that appropriate documentation was used. You pack them and send them direct from you to the FFL.
Spipping Services have very clear onLine info on firearms shipping requirements. THEIR Requirements are the ones that count. Find out what the Shippers Insurance limit is (you pay extra), so you don't pack to many handguns in one box that Insurance won't match. You can order cardboard rifle shipping boxes onLine, I think there are six per pkg.
Alternatively, you could find a FFL on your end and pay him Transfer Fees too plus what ever packing, handling, ship and Insurance.
It's really not hard to do, just have to get the prep work right.