Chech with your local sporting clubs as was stated. They often have shoots that are a great stepping stone to getting into higher level competitions. You can also check with the NRA and cmp to see if there are any shoots in your area.
I am in Detroit, MI. I am looking for some handgun competitions. I have heard about a few and cannot get in touch. I know competitions are afraid of Detroit. I am willing to travel to neighboring cities to compete.