I can tell you what I do, FWIW. When I come to an agreement with a renter, I send them a rental agreement outlining the cost, deposit, and cancellation policy. They return a signed copy with their deposit. Once I receive their final payment as per the agreement, I transfer the reservation to their name. The resort I rent most often provides me a form when I reserve my floating weeks. If someone other than I is to checkin, I put their name and other particulars on the form. I mail and fax (as a backup) the form to the resort. I also send a copy to the renter and request that they bring it with them at checkin.
After the renter checks out, I confirm that there was no damage to the unit and refund their deposit. The resort also will take the renters credit card for any incidental charges or damage, but I collect a deposit from them as well. If their credit card were no good, the resort would come after me for any charges.
You should certainly have some sort of paperwork as the renter. I'm sure everyone has their own variation. You are going on faith somewhat unless you decide to spend the extra money to use an escrow service.
If it makes you too nervous, you can usually also rent directly from most resorts. It's safer, though probably about double the cost. Still, it might be a small price to pay if you're going to lose sleep over fear of a problem.
I have also been on the other end when I rented from a member of the Timeshare Users Group. I just sent him the money via Paypal and he sent me the reservation forms in my name.
Sheila