You'll want to use tungsten when shooting indoors under most normal lightbulbs. You'll know that you should use it when your photos have a yellow cast to them - you can demonstrate this by taking an indoor photo without the flash and one with, and you'll find that the flash photo will probably shows the whites as white, while without the flash, you'll have a lot of yellow.
Digital cameras are often pretty good at determining correct white balance expect for tungsten lighting.
Make sure to remember to set it back to auto before you start shooting outdoors again.
This can be adjusted to a point after the fact, but it's best to get it right beforehand.
(If you're shooting raw, then you can forget the last few sentences - you can easily adjust white balance to your heart's content afterwards with no penalty.)