The Disney Vacation Club is a timeshare program where members purchase a quantity of points and then use them to make reservations at any DVC resort or partner program. The number of points required per room per night varies by season, day of the week, resort and room size.
What you do to rent points is find a Disney Vacation Club member who has points s/he isn’t using and arrange to use them for a certain amount per point. I usually go through the Rent/Trade board in the DVC section of the DIS or on MouseOwners.com, but you can also use a service like DVC-Rentals.com or David’s Vacation Club Rentals. You can find out how many points you need for your stay by looking at the points charts posted on the DIS or other online DVC member communities. For instance, say a reservation in a studio at BoardWalk Villas for Sunday-Thursday is 13 points per night. If you rent points at $11 a point, you’re getting your stay for $143/night—far below the $300+ rack rate.
It takes trust on your part because the member controls the reservation at all times—as a guest, you can’t phone up DVC and check on it. When you are thinking about renting from a member, check their posts on the DIS or MouseOwners to see if they’re a longstanding community member or someone who just signed up to rent their points.
Usually the member makes the reservation and sends you the printed confirmation from DVC, and you pay the member half the cost of your reservation (Paypal is good for this). Then you pay the balance a month or two before your arrival date—it depends on when the member would need to cancel the reservation to get his/her points back if you flaked.
If you want to add Disney’s Magical Express service or purchase one of the Disney Dining Plans, the member must make the arrangements for you (free Disney Dining Plan promotions are not available with DVC reservations because they are offered exclusively as part of a traditional resort room-and-ticket package for which you must pay full price).
Here’s a link to the Rent/Trade FAQs on the DVC board of the DIS and the Rules, Guidelines and Helpful Tips forum on MouseOwners.