Trap and skeet are both pretty simple...in trap, you stand at 16 yards from the house, while the clay throwing machine (the trap) oscillates randomly from left to right. You don't know where the clay will go, except that it will be in some direction heading away from you. Each shooter takes five shots at each post, which are numbered 1 through 5, 1 on the far left and 5 on the far right. After the fifth shot on a particular post, everybody rotates one post to their right until you've shot all the posts, for a total of 25 targets. Skeet targets on the other hand will always fly in the same direction and path, but you move around the field in a semicircle. There are 8 stations on the semicircle--7 on the arc and 1 (station 8) in the middle of the field--and you get different target presentations as you progress around. There is a high house and a low house, and you will shoot a single target from both on every station. Additionally, stations 1, 2, 6, and 7 have a doubles shot, i.e. one target from each house simultaneously. The same number of targets are shot as in trap, 25.
The best way to learn is to either watch the good guys, or if you are lucky enough to have someone who teaches in the area, take a lesson. Most clay shooters are more than happy to introduce new people to the sport, no price attached. As has been said before, trap and skeet throwers throw a faster target than a hand-launched trap, which can take some getting used to, but once you find your own technique and style, it becomes second nature.
