Let us know where are you located and we may be able to give you specific recommendations.
The best thing to do is to find a local club and get information from them. Most recreational clubs are associated with a racing team and they are generally the most welcoming to new racers. There are probably a number of pure racing teams near you also, but they usually assume that you have a little bit of racing experience. A good club or team will teach how to safely race -- things like holding your line, cornering, and protecting your front wheel. These are not skills that you will probably not pick up riding by yourself or in a tourist/club ride.
Another thing to look for are the race training rides. Nearly every major city has an informal weeekend ride that will introduce you to the local teams and racers. These rides are generally not sponsored by any one club or team, people just show up at some starting point and then roll out together. These rides are as close to racing as you can get without pinning on a number. They are very fast, aggressive, and potentially dangerous.
What kind of racing do you want to do? The road season ended last month and now cyclocross and time trials are in full swing. If that's what you want to do, find alocal one and show up. The road season will start again when the weather improves. Here in southern California that's the begining of February, but in New England that may be April. I believe mountain bike races will start again at the end of spring, but I'm not sure.
When you do start racing, you will be racing as a Catagory 5 on the road. You may also enter masters races if you meet the age requirements, but these races are often as fast or faster than the pro-1-2 races because anyone, even ex-pros, can and do enter masters races. Lance Armstrong could enter a masters 35+ race next year.
If your racing on the road, you will most likely be racing criteriums. These are short coarses that you will race around for 30 to 90 min. They are generally flat, held in industrial parks, and end in bunch sprints. You're first goal will be to finish safely in the pack. For "scrawny weaklings" like you and I this can be difficult. The first race you do the speed will probably take your breath away but don't worry about it, you will get better and you will get faster.
That's plenty for now
Sean