All you need to get started is a drivers license, a car that will pass tech, and the entry fee. Also a helmet if you have access to one that meets our standards (M95/SA95 rated or newer), but we do have a few loaners.
The course is set up using the oval and the infield. Here's a sample of one of the configurations, although it is different every time and we alternate directions at each event of course:
http://www.brightcove.com/title.jsp?title=1137755206
The day is broken up into heats that are about 2 hours each. In the case of Nov 4th, the schedule is:
7:00am gates open
11:00am reg & tech open
12:00pm course walk
12:30pm drivers meeting
1:00pm Heat 1
est 3:00pm Heat 2
6:00pm gates close
So you would show up, unload your car, go through tech, go through registration, walk the course, and attend the drivers meeting. Then you would drive in heat 1 and work (chasing cones, writing down times, etc) in heat 2... or vice versa.
Each heat is usually 20-30 cars. You line up and start at ~30sec intervals. You're never near another car when you're on the course, all you are trying to do is beat the clock. Usually you get somewhere between 6 and 10 runs in your heat. Results are handed to you on post-it notes so you can see your improvements, then afterward we publish everybody's results like this:
http://www.get-fast.net/nasacross/9907res.htm
As a nonmember who hasn't done it before, you would register as a Novice. Car classing is done two ways at Langley... either by NASA autoX classing for NASA members, or by SCCA solo classing for everyone (but if you're a Novice, that's your class... you'll only compete against other Novices in the final results, but your overall ranking will be listed too.)
NASA car classing is essentially like... each car starts in one of ten base classes. Points are added for modifications and when you get 20 points you bump to the next faster class. Pretty much any car with a non-factory turbo setup will bump at least 1 or possibly 2 classes up, depending upon what all has been done. Usually you are only technically competing against other people in your class... but you'd need to be a NASA member to worry about that. SCCA classing is its own thing with its own huge rulebook. Stick with "Novice" for now and you won't have to read it.
Pre-registration for these events is recommended to make sure you get a spot, although some people do just show up that morning:
http://www.nasaproracing.com/nasa_ev.../?event_id=501
Many further details are on that page as well (including the link to the tech inspection requirements.)
Thanks for asking,
Jon