Rallying is a sport which generally involves driving on normal, public roads. There are a number of different sports gathered together under this banner, which are generally subdivided into the categories of Road Rally and Stage or Pro Rally. The former is a sport conducted on open, public roads at legal speeds and in conformance with all traffic laws. The latter generally involves closing roads in order to allow a high speed motor sports event.
There are a couple of ways to find a local rally program. You might want to visit the SCCA Web Site and see if an SCCA Region near you is on the net. Rally Central has an excellent "rally finder" service, and the Rally page for the Detroit Region of the SCCA has a lot of Rally links. Finally, check out the Other Links page to see if you can find nearby clubs.