I'm no expert, and pretty new to this myself, but I agree with WildWolf - Tv mode if you want to freeze (fast shutter) or blur (slow shutter) motion, and Av mode most other times (low F stop for blurry backgrounds, higher F stop for more of the image in focus). ISO is important too, but I generally get away with 100-400 outdoors in the day time and 200-800 indoors with lots of light.
What's good about Tv and Av (for a beginner like me!) is that whatever value you set for the shutter speed or aperture, respectively, the camera automatically selects a good corresponding value to get a good exposure. E.g., you set a fast shutter to freeze some motion, and the camera goes with a wider aperture to get enough light to expose right. In contrast, using straight manual mode (M), it's all on you to choose both of those - a much trickier task for my inexperienced mind.
Of course, you can bump into limits of the lens - aperture can only go so wide, and this can mean dark photos if you set shutter too fast with insufficient light. Similarly, if you set a small aperture when there's not enough light, the shutter value will go so slow that your image will be blurry if you try to hold it in your hand. You'll learn all about working within limitations, too, which I've found useful.
Also, jimsolt's suggestion is really great too. I started doing something like that on my A80 before I upgraded to the rebel xt. Just pay attention to the information about the shutter / aperture / ISO settings the camera is choosing for you in automode and use that as a starting point (in playback mode hit the info button a few times until you see the histogram - also good to know about!).
Oh one other thing - if you have time, learn to read the histogram. This will help you figure out if your exposure is about right even within the limitations of the LCD playback screen.