Every aircraft listing carries a box, under Questions and answers, with FAA forms for the sale: AC Form 8050-2, the Aircraft Bill of Sale, and AC Form 8050-1, the Aircraft Registration Application, with the FAA’s own page of registration forms and fees. Each opens the FAA’s page.
The rules that matter in a purchase are 14 CFR Part 47 (registration), 91.409 (inspections) and 91.417 (maintenance records).
Hangar Flying takes no part in the sale. Before you pay, use an escrow agent and have a pre-buy inspection done.