Oh, can I empathize! One place I lived had those big black ants that were all over my kitchen sink, counters and dishwasher. I finally called the exterminator who found a huge nest of them in the roof of my garage. (You could actually HEAR them chewing.) Ugh.
Then, when I moved here I've had teeny tiny ants all over my kitchen. But I found a cure. Local hardware store recomended Terro Ant Killer. It's a liquid and you only need a drop or two. The ants cluster around the drop of liquid -- and then they all disappear. I guess different kinds of ants respond to different poisons, but this product definitely fixed my problem with teeny tiny ants. (Don't think it gets rid of the big black ants. but upi can give it a try.)