Good question. There are 2 main types of chokes- jugular (blood) chokes and throat (windpipe) chokes. These come in the form of Gi and no-Gi chokes. Since you are talking about MMA, I assume you would like to know about the basic no-Gi chokes first.
1) The rear-naked choke is a jugular (blood) choke because it cuts of the blood circulation to the head and causes someone to quickly pass out within a few seconds. From behind, you reach far around the neck of the person, making a "V" shape with your forearm and bicep. The bicep crosses one jugular, the forearm crosses the other. Grab the opposite arm's bicep with the arm that in a "V" shape, and take that "free arm's" hand and place it behind the head. Also, known in pro-wrestling as the "sleeper" hold. The choke comes from pressure on the back of the head, and the squeezing of the "V", making it a tighter "V". The blood cuts off quickly, the person sees stars, but it usually doesn't hurt very much. Most people "tap out" not because of the pain, but because of the panic they get when they feel themselves losing consciousness. Here is a pic:
http://www.nd.edu/~judo/hadakajime.htm
2) Throat chokes on the other hand hurt like hell and cause the throat to close, preventing air to enter the lungs. Most people tap due to the pain, and panic of not getting air into the lungs. From behind, take one arm, and cross the forearm across the throat, straight across, not angled. You should lean to the same side that your hand is on, pushing your shoulder forward (the same arm as the hand) and pull your hand back. Take your free arm and clasp your hands in a typical wrestling clasp. Again, the pressure is applied by "closing the V", but this time, the angle is such that the pressure is on the front of the throat and on the back of the neck. Throw your shoulder forward while pulling back on your hand. Here is a good drawing of that:
http://judoinfo.com/images/shime/hadaka_jime.gif
Here is some more info:
http://judoinfo.com/chokes3.htm
PS- These two chokes are both called the "hadaka jime" in Judo, but they are definitely two different techniques. Learn them both.