Everyone else is correct about the sponsorship fees. They are as much to seperate the serious pilots from the dreamers as they are to fund the operation of the aircraft. Once you join a wing, you will get to know the wing's officers, and whoever is in charge of checkouts will be able to give you guidance.
A lot of pilots think they can use the CAF to put them in their dream machine- that they can pony up $10,000 and strap on a Mustang or a Corsair. Flight sponsorship of the fighters is very different from flying the trainers, transports, and bombers. There is an interview process, and they usually start looking at people when they have over 1000 hours in high-performance singles (and by that, I mean T-28s, AT-6s, A-1s, and the like). A P-51 is obviously a lot of airplane, and they want to make sure you have plenty of experience before they entrust you with one.
There are a lot of great people invoved with the CAF. They range from people who aren't pilots but are interested in WWII history, to retired and current airline pilots. Getting to know people in the local wing is the best way to get involved, and it sure helps if you have the time to help out. Most wings have a monthly meeting, and on weekends they meet at the hangar to BS, do chores, and perform maintenance. Those old airplanes need a lot of maintenance- sometimes hundreds of man-hours for every hour of flight, so sweat equity is one of the most important contributions you can make.
You can PM me if you have any other questions. I've only been in the CAF for a few years and I'm not a flight sponsor yet, but I'm planning to be soon- probably this summer!