The flash is the biggest solution to low light digital photography. However the problem with this is that not all situtations can benefit from using the flash. Not only does it interfere with your "moment" socially and artistically, but the flash can flatten out your digital images. This is especailly true for a flash that is built-in on digital cameras. The built in flash (and a flash in general) has the effect of lighting your subject on the front only which compresses the depth of your subject in your digital photography.
This can be avoided to a certain degree, depending on your subject and by watching how your light falls. Learn how to see hoe the light falls on your surroundings and your mind will become adept at knowing what works and what doesn't with the flash.
Really, a good way to combat the problem in low light you can try using a higher ISO. Your ISo simply means the amount of sensitivity of light falling on your sensor. For example take traditional photography as a comparison to digital photography. Traditional photography ISO will be film sensitivity. (ISO in traditional terms works with film speed as well.)
The only set back in digital photography ISO is noise. If your ISO is perfect for the photo yet there is significant increase in noise you can use software to sharpen up your digital photo.
Being a photographer, it's about catching those moments. Which means, we do not want to have to use our pop-up flash...if we don't have to. Low lighting conditions not only set a certain mood, but the light gives off a color that may not be replicated anywhere else. Upping your ISO can do the trick but if not, read more from this article. Where you can learn about, even removing the digital noise your camera catches.