Basically, you expose for the ambient ("existing") light however you want, and the flash will automagically provide the rest of the light needed for a proper exposure (for values of "proper" as decided by the vagaries of your camera's metering system).

Your flash photo in effect consists of two separate exposures; one that sucks in the ambient light in the room and one that captures the light blasted out from your flash. The sum total of the two is your photo; how you balance them decides the mood.

To take this to one extreme: If you do not want to use the ambient light at all, use a low ISO, a fast shutter speed, and a small aperture. The ambient part of the exposure will come out pretty much black, and you will have an almost totally flash-lit picture. (It will probably be rather sucky.)

To take it to the other extreme: If you want to rely almost entirely on the ambient light, use a high ISO, a slow shutter speed and a large aperture. The flash will now only give a very little 'lift' to the total exposure of the photo, and you will get spades of atmosphere from your candle-lit dinner or whatever it is.

Properly balancing the ambient part and the flash part of your total lighting is much of the trick of getting good flash photos!