The light indoors is never really that great. Fill-in flash is almost always a must. The goal is to achieve even illumination. Even with today's CMOS Sensor digital cameras, one can sometimes only shoot at only 1/2 sec., which results in some horrendus camera shake and motion blur. The solution to this, of course, is to use flash, or a faster lens if you can afford one.

The key to indoor photography is to get a flash that you can bounce off the ceiling or wall behind you. Your on-camera flash will direct the light directly towards the subject, resulting in pictures that people immediately recognize as being taken with flash. i.e. harsh shaddows. Bouncing the light off the ceiling or a back wall almost completely eliminates this effect. Some use an attachemnt to their flash which diffuses the light (a flash diffuser) to get a simmilar effect.

Use a long focal length. This will make your subject's face look more natural, and will help in blurring the background.

Speaking of blurring the background, for a good portrait, use a wide aperture to minimize depth of field. This coupled with a non-distracting backgound will result in a better portrait.