Autocross is an extremely inexpensive and safe way to participate in competitive motorsports. In general, any safe, street legal vehicle can compete without any significant modifications (although heavily modified vehicles may be at a disadvantage due to the rules structure -- a heavily prepared, supercharged drag racer is unlikely to make a good and competitive autocross car.)
Autocross and Solo II events are "Time Trial" style competitions; there is no wheel to wheel racing involved, as cars are sent out one at a time, or at least spaced out so that they should not come into any contact with each other. These events are derived from the original Gymkhana competitions from 50s and 60s. Today, an event called a Gymkhana is usually a "fun" event, with slow speeds and silly tricks. An event called an Autocross or Solo II is usually a serious competition, with speeds perhaps as much as 70mph in large lots or on airport runways.
In general, a course is laid out using traffic cones; time penalties will charged for disturbing cones. For most clubs the penalty is 2 seconds per cone, although for some it may be 1 second.
In the Discussion Area you will find an discussion topic devoted to Autocross.
See the Autocross Links page for a list of some other extremely valuble pages on Autocross.
There are a couple of ways to find a local Solo or Autocross program. You may want to visit the SCCA National web site and see if an SCCA Region near you is on the net. There are often non-SCCA clubs which put on Autocrosses in various locations, and some of the links on the Autocross Links should be able to help.