The best way to start autocross is to just show up to an autocross and drive Unfortunately, you're going to have to wait, and you'll have to drive a ways to get to most events. There may be something in Maryland or WVA I'm not aware of, but the closest events for you in VA would probably be DC (WDCR). BRR-SCCA rotates between a number of sites, the closest to you would be Verona. Most everyone in this part of the country has wrapped up for the winter, but NASA-MA usually has a winter event near Richmond in January.

Otherwise, check the websites when next year's schedules are published, and just go! Autocross is a very novice-friendly sport; you don't need any special safety equipment, just a car in good condition (tires aren't corded, battery's secure, you're not spraying oil everywhere, etc.) and a helmet (Snell M2005/SA2005 or newer). All the local clubs have loaner helmets you can use if you don't have one. You'll need to clean your car of all loose objects, including your floor mats, but that's about it for prep.

http://www.brr-scca.org/
http://www.wdcr-scca.org/