I've rented points 3 times in the past for a 1BR suite at the Boarwalk villas.
At it's simplest, the process would be something like this:
First thing you'll need to know is how many points you'll need to rent.
Use this calculator to check different DVC resorts and room types to see point values for your travel dates. Sun-Thurs rates are the lowest, along with the typical "Disney season" rates. (ie: value season will be the least amount of points).
You'll probably wanna pick 2 or 3 resorts cause if you're within a couple months of your trip, availability can be slim sometimes. So giving a DVC member 2 or 3 places to check is always good cause the DVC member has to phone DVC Member services to check for rooms.
Once you have your points,
look for a renter here (will need to register I think). Pretty much just find someone renting how ever many points you need at a price you'd like (I never go for anything over $10/point) and send 'em an email with your request. (ie: 1BR at BWV for such and such dates).
You can ask for references, contact info, etc... from a renter too.
The DVC member will check availability, and book it if you agree to it. Most will accept payment via paypal. That's how I paid the 3 times.