Fencing is really three sports, as there are three weapons used for fencing:
Each weapon has different rules and different target areas (areas on the body where a valid touch can be scored).
However, the basics of fencing are applicable to all weapons. Most fencers learn to fence all three weapons, but tend to specialize in one.
In general, the goal of a fencing bout is to score five touches on your opponent before he or she can score five touches on you. How to achieve that is where the fun occurs!
Fencing.net has a wonderful Introduction to Fencing. Other sites of interest are the Usenet Fencing Frequently Asked Questions (FAQs) and/or the WikiPedia Fencing entry. To watch some fencing, you can always check out Fencing on YouTube.
Please ask Phil or any of the veteran fencers at the club if you have any questions. We love to answer your questions! (It let's us think we're smart) :-)