First of all, the weather needs to turn warmer. Around May, the Detroit Council of Sport Car Clubs will hold an autocross. So will the Detroit SCCA, but those aren't very well-run, and you spend a lot of time standing around and little time racing.
Sign up for a DSCC event (http://dcscc.blogspot.com/). The night before the event, clean your car out, completely. Check the fluids, and air your tires up to about 40 psi. Take a yellow crayon and a tire gauge to the autocross, along with a chair and food/water. Also, take masking tape to make numbers for your car.
The day of the event, get there early. Follow directions. Put the numbers on your car. Find someone else in your class who may help you follow the directions, as they may be confusing the first time. Walk the course, either with this person, or follow behind. Make notes while walking, if only to help you memorize where to go (no bother knowing the best way; you'll need to know the right way first).
Color the edge of your tires in three places with your crayon, while you're waiting in line to race. Small marks work as good as big marks, and don't look as hokey. Drive the course when it's your turn (most organizers will loan you a helmet).
Afterwards, look at the crayon marks, and ask someone else to advise you about your tire pressures. They'll tell you to raise or lower, and you'll have your gauge to help you do so.
After racing, let your car cool down and check your to see how you did. Before going home, lower your tire pressures to the proper level.
Go back to another autocross soon after. At that one, worry about how to go faster.
It will cost you about $40 or $50.