The first thing to do is go down to local track and get an application for Endoro race or whatever entry level racing your track sponsors.
Get your self a hundred dollar car that will fit the entry requirements pay the entry fee (make sure you have a good job because it cost a lot of money). And race your car on race day. Get connected with the drivers at your local track the veterans can teach you a lot about the ins and outs of racing.
After you get the feel for the track and learn more about racing and race cars., and build a circle of friends that are enthusiastic about helping out (pit crew for the early racing). You will want to go up to the rank at your track. MORE MONEY will be required , to build a car for that division. Eventually you will have to hook up with some sponsors, they may start with one that will cover your entry fees or tires for race day.
You will always want to keep an eye out for donations like trailers, tow trucks , and car parts. Having a big back yard and a garage is almost required also.
The main thing to remember is to have fun, because the number of drivers that make it thru the ranks, is very small and usually take time. For every Kyle Busch there are 50000 wanna be's. So remember to have fun and be courteous to everybody at the track you never know where the help you need to make the next race or just get past someone on the track is going to come from.