First, clean up. Put any fruit or other food that is out into the fridge. Clean counters, take the trash out.

Second, bait them. Take a small bowl or ramekin, put a drop or two of dish soap in, put an inch of apple cider vinegar in and briefly stir. Leave it out on your counter wherever you've seen them concentrating.

The apple cider vinegar attracts them, since the rest of the kitchen is all nice and clean now. The dish soap reduces the surface tension, so they land to grab a drink and sink. The bowl will be pretty gross in a day or two. Empty out and repeat as necessary.

I suppose moving is out of the question?

Besides cleaning your counters, make sure to clean your garbage disposal if you have one. You might even want to buy the packaged 'disposal cleaners' because they really clean things up. There may be small bits of food still trapped in the disposal that they are breeding off of. DH had this issue in his previous apartment and it took a couple weeks for them to all die. We also bought fly paper and hung it around the kitchen.

Vacuum them out of the air. Use the attachment hose and just suck them out of the air and off of the different places they have landed. That was the fastest method for us. Bait them also to catch the leftover gnats.

Also check your houseplants as a possible source, if you have any. They might also be coming from the soil there.

So, glad you posted this. I have had problems on and off for the last year. I read about drain gnats and one of the solutions was to poor Clorox down your drains. I think it helped, but it ruined the silver on some of my drains, so I don't want to do that again.

My in-laws had this problem. They finally figured out that the gnats were coming from some dried flower arrangements that were hanging in the next room.

A friend of mine had little flies--couldn't figure out where they were coming from. Everything was cleaned everywhere...

Finally, one day she opened under the sink and cleaned out down there to discover her disposal had a leak and had been leaking into the undercabinet (was ruining her floors, etc).

Besides the new kitchen that resulted from the water damage insurance claim, the little flies were gone after everything down there dried out (and before insurance tore everything out).

So, besides checking IN the drain, check UNDER the drain.

I only have gnats when I have over ripe fruit on the counter or a rotten potato under the sink :).

When I get rid of their attraction, they go away.