Dave gave you a good link which mentions both the SCCA and NASA. I would say they are the two groups that put on Autocrosses in large numbers. NASA started on the west coast and is better known out there but they do have a very large chapter based in VA (
www.nasaproracing.com). Check out the SCCA website and find your local chapter hopefully they have a good website which should give you all the information you need to go to an autox drop about $35 and drive your car like you never have before. Like Dave said, do it and have fun.