2 Answers

Killing gnats with dish detergent: add small amount of the detergent to water and water plants in your home with with it. Detergents kill larvae of gnats.
Killing gnats with sugar: mix water with sugar in a small bowl, cover the bowl with plastic wrap and poke small holes in it. The smell of sugar attracts gnats, they enter the bowl through the small holes but are unable to get out of it, and eventually they die.
Killing gnats with vinegar is done the same way as with sugar.

By gnats, do you mean fruit flies?  If so, you can kill them and eliminate the source, fruit or vegetables that are sitting around or spoiling.  And yes, the above mentioned methods will work for fruit flies also.