Tips, anyone?

I can take decent pictures if I have natural light outside. But inside, my pictures are not all that great. I find my camera flash just makes my pets fur look weird and their eyes glow. So I try lamps/lights. Half of the pictures are blurry still.

What are the best lights to use? Watts? What about flashes...Those big ones you can stick on top of the normal flash. I have seen a photographer use one and sort of bend it up a tad so it doesn't hit their eyes...does that work well??

Any suggestions welcome