Essentially, you're paying a
DVC owner to make a reservation for you. They will control the reservation right up until you check in, so a bit of trust is required.
Points are the "currency" that owners use to make DVC reservations. The number of points the owner has to "spend" to make the reservation depends on the resort, the room type and view, and the time of year. The owner sets the price per point that they will charge you to make the reservation.
There are a couple of ways for you to do this. You can find an owner and work with them directly (see our DVC Rent/Trade board for that), or you can work with a broker like dvcbyrequest.com. They act as a middleman, find you the owner who can fill your reservation, handle all communications with the owner, and handle the money. They're a bit more expensive, but I think well worth it, especially for someone who's new to renting.
Probably the most important difference between doing a rental and booking a room through Disney is that with a rental, you can't change or cancel your reservation. Well, you can, of course, but you won't get your money back.
The next most important difference is that DVC owners book EARLY. So, in order to have the best shot at getting what you want, you need to be starting the process about a year out.