The best I've seen is to take pictures "unconventionally".
Instead of just standing there and taking all your pics from head level in landscape mode with the subject dead center....change it up. Get close. Get low. Get hi...err, get taller. Put it in macro mode. Have the frame mostly empty, with subject off to the side. Make a normal everyday photo subject look different, let people see it in a way they haven't before.
Oh, and the beauty of digital is that you can take a LOT of photos. So snap away like crazy, you'll be able to not use the bad photos later. Just get lots of shots from different angles with different settings.
I think dpreview.com is the Official Home for Photo Noobs. Check it out if you haven't already. They have forums you can read endlessly, and one of them ("Canon Talk") is basically devoted to Canon's compact cameras.