somosomo gave good tips so I won't repeat them except that a tripod is a MUST for great shots...but beyond that fuzzy photos can also be caused by the sensor that reads distance for your auto-focus bouncing off the glass instead of your intended subject. Backing up further helps (more depth of field by your camera's defaults), so does putting the lens RIGHT on the glass..you can sometimes use the flash when you do that too.
It doesn't look like your camera has a manual focus option so that's out.
Odds are though it's just camera shake and the shutter is open so long for the low light shot that the shake is obvious in the results. If you dont have a tripod do whatever you can to stablize you and the camera. Be carefull that when you push the shutter release you're not moving the camera..a common problem for people who don't know how to hold a camera right.
...Even with the regular digital cams you need a stable base to rest the camera on so that the hand pushing the button is not doing anything but pushing the button. ie....it's not holding the camera up and stable AND pushing the button which you see ALL the time and is OK if you're not taking low light/no flash/ long exposure shots! Holding a digital camera with 2 fingers from your left hand and 2 fingers from your right hand with one of them pushing the shutter release makes it very easy to twist the camera up and down when pressing the shutter..not to mention you need to hold your arms extended and still! Yikes! Works fine for normal shots...but not so well here.
If you ever watch a professional take a photo he/she has one foot pointed front to back, the other left to right to stablize his/herself....the left hand is palm up supporting ALL the weight of the camera and controlling zoom and the right is only barely holding the camera and pushing the shutter release. It looks silly to take shots like that with a compact digital because you have a display that needs to be a foot from your face instead of a view finder..and your camera isn't as heavy as a DSL with glass lenses so it's not AS needed...but it can help in low light if you can't use a flash.
Try it..see if it helps...but you're much better off getting a tri-pod!
And tell the tang to hold still...
No matter what you do, if the subject is moving with a long shutter time it will still be blurry.