First of all, go to the Rent/Trade Board in the DVC Forum as there's some stickys at the top with lots of great information.
It's really not that complicated. However, there's lots of trust involved because the owner you rent from retains control over the reservation even after it is put in your name...so you must have someone you feel comfortable with throughout the transaction.
Basically you just decide what dates you want to travel, where you want to stay, and what type of accomodations you need (studio, 1bdrm, etc). Then use the point calculator in the link provided at the top of the DVC forum and determine how many points it would take for your length of stay. Points run anywhere from $10 and higher. There are no room taxes, so the price quoted is all you will pay. You can however, choose to add the dining plan which must be done by the owner -- but you pay for it at check-in.
Once you have all the legwork done, either reply to a post by someone with points to rent, or start a post of your own (you'll see lots of examples on the R/T Board). When you find someone to rent from, they will work with you to see if there is availability and will give you information on what their payment terms are -- if you feel it works with your particular needs, then go for it!
Some of the most important things to remember are that you don't get daily housekeeping when renting points (I believe you get fresh towels and trash emptied on the 3rd or 4th day and a deep cleaning later depending on total length of stay). Also, you don't have as much flexibility if your plans change due to the cancellation/change policies imposed on the owners by DVC.
I'm sure others will chime in with more specific information but I just wanted to provide a brief overview.