Natural light thru windows if you can get it. I don't have good light (with a black dog!!) so I deal with this issue. A tripod is great for still subjects but you will still get blur if the subject moves.

For a faster shutter speed under low light raise the iso to 200 or 400. Higher ISO will be grainier picture so keep iso as low as possible to maintain quality.

Accessory flashes (I want one) are good for avoiding red eye or dog glow eye since they are higher above the lens and people and hopefully pets will not look directly at the flash. Angling the flash towards the wall or ceiling bounces the light off the ceiling/wall allowing for softer indirect light. Bounce light is best off white walls to avoid a color cast.

Also consider white balance. If you use various lights for more light, stick with 1 type of bulb like incandescent of fluorescent. You can then adjust the white balance for the type of light you are using if auto white balance gives a color cast.

Hope that helps!