The number one mistake that I see people make is not holding the camera still. So many photos turn out blurry for this reason. Many cameras are getting blamed for bad technique by the photographer.
You may say "well duh", but if you make the conscious effort you'll notice your photos are just a little more sharp.
When the flash fires or if you have really good light you'll get some non blurry photos even if you happen to jiggle the camera but practice holding still and you'll start a good habit.
So hold your camera still, let me know if your photos improve.
This photo below had plenty of good light. If you look at the enlarged version you'll see that it isn't blurry because of bad focus. It is blurry from camera jiggle. Check it out zoomed in.