Don't waste your money going through an FFL, it's real simple, Google the following: DPS-3-C you will find the form in fillable PDF format on the state website, you will need 4 copies so fill out the sheet (both forms) and print it twice. Then Google DPS-67-C you will find the fillable PDF for that, you only need one copy, unless you want to give one to the buyer but it's not required. Once you have the forms filled out call the DESPP at the number on the bottom of the DPS-3-C and tell them you need an authorization for a transfer, they will ask you if it is a handgun or long gun, then they will ask for your permit number and the buyer's permit number, they will tell you to hold for a moment and then will come back with the authorization number, put this number on all the forms. Now, take one DPS-3-C and give it to the buyer as a receipt, you keep one for your records (20 years, just throw it in with your gun receipts or other important papers that you won't toss out), one copy goes to the DESPP at the address on the bottom of the DPS-3-C and the last copy goes to the police department in the town the buyer lives in. The DPS-67-C should be kept with the DPS-3-C that you are "storing away". FYI, if you transfer a gun to an FFL they will give you the DPS-3-C from that transaction, you need to keep that for 20 years too, it doesn't matter who you transfer to..
ETA: I just realized you are the buyer, everything I wrote above is the Seller's responsibility, you take your one copy of the DPS-3-C and your done, you do not need to keep it at all by law but it's good to have a receipt for a gun you purchased.