Some basics for composition--
Avoid centering stuff dead in the middle of the frame. Really, this is the most important thing to remember. There are exceptions to the rule, but generally speaking you just don't want to drop your subject dead in the middle.
Hand in hand with this is a second idea, that you should only put in the frame that which you are photographing. This seems like kind of an obvious one, but it runs deeper than you may think. How many snapshots have you seen where the subject is just a small part of the whole picture, and the rest of the frame is just the boring random stuff that happened to surround the subject? There are lots of ways to avoid this, but the most straightforward is to just get closer to your subjects than you would have done. Now, this is different if you're trying to show place/context/whatever, but not filling the frame with their subject is a very simple beginner composition error.
Another idea connected to these is that you generally want to have your action leading into space-- as in, a car on the left of the image should be driving towards the right, a person on the right should be looking left, etc. This draws the viewer into the image and holds them rather than leading their eye out of the frame.
One more thing to think about is checking for background elements that will distract from the final image. We see in 3-D, which means that it's easy for us to ignore a pole or plant behind someone. But when it is compressed into 2-D, background stuff can merge with people and look very bizarre. Keep an eye out for where this stuff is and how it is affecting the image.
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