Road Cycling Racing
Most local cycling organization will host a few road races throughout the year. They probably aren't as high profile as many of the professional road races, but they are the place that all racers got their start. The best thing about racing locally is that you are riding on the roads that you already know. That means that you can practice on your own time before the actual race to get a feel for how the race will go down.
The most important piece of equipment is (obviously) your bike. If you currently cycle for fun or exercise, the road bike that you are riding will probably work out great for road racing. The key to success is durability when racing. Unless you have a sponsor and full team, you probably don't have a car with parts and a backup bike trailing you. What you need is a bike that is not going to fail on you in a race, as well as solid tires and tubes that aren't going to give you problems under racing conditions.
While it's only a basic level of gear that you need to begin road cycling racing, you have to be in good shape to start. Ride the course beforehand (if possible) to make sure that you're capable of making it all of the way through a race!