You pay seller, seller gives you a signed receipt that specs the handgun (bbl length, caliber, s#, pistol or revolver, manufacturer) and confirmation of sale.
Take receipt to clerk and pay whatever to have your permit amended.
Once that is done, take ticket from clerk, trade ticket to seller for handgun.
Ideally you and seller would be at the clerk's office, that way the clerk can get the info, the seller can get the ticket for his records and you both can get your permits amended all in one pop.
Or at least that is how it works in Jefferson county.
YMMV, not responsible for lost or stolen items, keeparms and feet inside the carriage at all times, etc.