The hardest part about any kind of racing is finding races near home, and getting the nerve up to go do it.
Use the 'net search engines to locate races.
USA Cyling is the main organization for bike racing and you can find many races on their "events search" link. Also, look for VeloNews at a newstand. It is a magazine dedicated to bike racing. The back of the magazine has race listings for the US and Canada by region.
Getting up nerve is another thing. The best advice is fubar's - just go do it. Don't let the expensive bikes and fancy jerseys of the other riders intimidate. Go to have fun first and keep your expectations in line.
Race in the beginner class to start. You'll need to buy a one-day license - $15 - and pay an entry fee, another $25-35 usually. If you think you'll race more than 3 times during the season, it's more affordable to get a regular NORBA racing license.