I'm not a professional photographer, but I would think that for best results you need very good lighting (preferably sunlight), and if you don't want to use the flash, you can look into an image stabilization system. It should get rid of the "blurry" effect (especially if you don't have a tripod).
I have a Canon Powershot with an image stablization system (A570 IS, just like Sanibelle!), and it seems to be better than other digital cameras I tried. Other companies than Canon have image stablization, it's getting fairly standard now.
The Canon Powershot keeps improving every year, depending on your model number if might be a very different camera than mine. My boyfriend has an old Powershot and it doesn't give the same pictures at all! Look at your model number and look at the specs before you buy a new one!