"Gnats" is a broad category. Whether gnats or not, you could simply vacuum them up.

We can be more specific if you tell us where they are (kitchen; closet; potted plants; or?) and what they are doing.

Where are these gnats located? Do they seem to linger around your houseplants? Are they in the kitchen with the produce? Or are they in the bathroom? Knowing what kind of 'gnat' makes a real difference as to the suggestions of control.

They are throughout the house but mostly in the kitchen area. I empty my kitchen garbage every day & don't have exposed food out. As I'm sitting at the computer which is located in the basement away from the rest of the house I see them here - help!

First, are you absolutely certain they are gnats? Or could they be small moths?

If small moths, you have a pantry pest in some of your dry goods -- cereals, flour, wheat bran, or more.

"Gnats" in the kitchen most often are really grain (Meal) moths. All grain products are allowed by the FDA to contain small quantities of moth eggs and feces and if your grain products are not stored properly (ie, in the freezer) those eggs will hatch and eventually those larva crawling aroung in your grain products will become adult moths.

Here is a link that might be useful: All about meal moths

If they are not gnats but small moths, what should I do? I am going to take all the food out of my cabinets & put any partially used items in closed contianers. Could I put moth balls in the cabinets with the food as long as the food is in closed containers?

No mothballs! Not anywhere near food/edibles!

If they're grain moths, you need to inspect all possible foods, among them grains and cereals, birdseed, and dog food.

When critters are found, discard that item.
If susceptible food is clean, put it in secure container -- glass with screw lid, or rigid plastic.

Then remove everything from the cabinet/pantry, wash down all surfaces. If shelves lift out, do so and inspect the 3 edges which touch the cabinet walls. Remove any webbing and critters found.

Next, purchase a pantry pest trap (several brandnames are available) from a drug store or hardware store. Use as directed to catch any stragglers you missed while cleaning.

Look at all of the grain products you have to see if there are larva in any of them. If you do find them, there have to be some it you have adults around, you can compost the infested grain product or toast it in the oven at 140 degrees for a bit, provided you would not object to having ome extra protein in that product. Do not use moth balls for anything excpet as listed on the label. Moth Balls are a class 1 carcinogen and not something to unnecessarily expose you or your family to.
Once these have been taken care of and to prevent future infestations store all grain products that will not be consumed in one week in the freezer.

Drain flies or gnats is another pest around areas with plumbing. My friend had a problem for a long time and finally discovered a small leak in back of her dishwasher.

Here is a link that might be useful: Drain flies fact sheet