Capturing moving pictures without blur

Hi. This is my first post and I should warn you I am in no way a professional photographer. But I thought I got a great camera particularly for my own art references due to the fact that I'm an Illustrator and Graphic Designer. I also have a nephew on the way and wanted to get the best pics possible that I could afford.

We all know babies don't stand still for pictures. So when I started taking pictures with my Sony Cybershot W-170 I realized that not only did my subject have to be perfectly still, but I did as well. I can't just take a picture of someone slightly moving without them coming out blurry.

I'm wondering if anyone is familiar with this camera and can possibly tell me if there's a way to prevent this from happening. I turned up the ISO but it ends up looking "fuzzy". Am I screwed and bought a camera that is only idea for still shots?

I'm guessing you are trying to get shots of the baby indoors. No point and shoot camera is truly capable for low light work. Your best bet would be to move outside; the best light would be during a cloudy day, or in patchy shade. If you are stuck inside, do what you can to get the baby close to windows. The flash is also your friend. It will help "freeze" the action, although the harsh lighting will likely not be as pleasing as natural light. Good luck!

Shooting babies indoors with a point-and-shoot is tough. Light is the key. Spontaneous photos of a wiggly baby in a dark room are simply unrealistic. You can use the flash, of course. But flash photos usually look a bit harsh. cm_mtb's suggestion about taking the baby outside is a good one. You can also set up photos next to a big window. Window light is wonderful for portraits.

1) Increase the camera's ISO setting.
2) Increase the light, 500 watt work lights work
3) use flash, like Photo-John said "flash photos usually look a bit harsh" you can add a diffuser or use bounce flash
4) spend more $$$ for a DSLR with a FAST $$$ lens - only if your rich :D

Don't totally throw out the idea of flash because of the harsh lighting. Pictures I took of my niece turned out fine with flash....something about perfectly smooth skin.