The best way to learn about fencing is to go to a tournament and watch. If you go to the USFA's tournament site
you can find what's going on in your area.
Where to start? This page
can tell you essentially all the rules, so I'll go more into the training.
The standard way of learning to fence involves footwork alone for several months before they put a blade in your hand. It's a very unnatural position, essentially a crab-walk, but if done well, good footwork will make hitting you much harder and hitting them much easier. Unfortunately, a number of people don't have the attention span for this, and it is very difficult to teach a quarter of the class the basics while trying to drill bladework with the rest, so most fencing schools have started introducing the blade very early. The only people I know that do that anymore are parents (start the kid at 6, get him to the Olympics by 30) and universities. Universities have the advantage of the semseter system to teach beginners essentially one group at a time for an extended period.
Now about bouts, things are fast, too fast. Sometimes you will blink and miss seeing who hit whom. Therefore, the best bladework is just large enough to beat your opponent, so no slashing, no windups, just reach out and poke someone (which also happens to be my name for a style used by several epeeists). Therefore, it can be boring to watch, but heartpounding to play. As you get better, you begin to find that nothing you do can possibly get through your opponent's defense, so tactics give way to strategy, making them mess up in a game of physical chess. I enjoy it very much, and I think you will too.The USFA also will direct you to schools in your area
I hope that's enough.