I have a few tips, as an owner of a 300D and a Rebel G 35mm.
Leave the camera in P (Program AE) mode most of the time. That's best for outdoor shots in daylight and for most indoor shots with flash. It's also good for long-exposure tripod shots at night.
Learn how to change ISO on the fly. That's been the most useful feature of the 300D for me since I bought it, compared to my old Fuji digital or my Rebel G 35mm (I usually leave it on 400 for daylight shots).
Get a pocket-size tripod for long-exposure shots. You might also consider buying the IR remote control (only about $25) so that you can make tripod shots without shaking the camera.
Don't try to learn everything at once. Learn one feature of the camera at a time, then move on to something that builds on what you learned before.
Most of all, don't concentrate too much on the science of photography. Shoot what you see. Sometimes the shot won't turn out, and sometimes it will, but the most import thing is what you see, not how you capture it.
