The key to killing ants is to do a broadcast treatment instead of treating individual mounds. If you treat just the mounds, new mounds will form in a few days because there are always some 'less active' mounds in the area that you don't see.
Talstar (bifenthrin) is a good product to use for broadcast treatments. It is fairly inexpensive and is safe for pets and humans. And it works quickly, within a day or so. It helps to water it in after application, or spread it just before a light rain. It is also better to apply when the ants are active, which us usually in the morning or late afternoon. However, it does kill many other insects. (such as worms, mosquitoes, fleas, etc.)
There are many baits available and they work very well. Baits are more specific to ants and will not kill other insects. However, baits can take a long time to kill the mounds, because the bait (poison) is taken to the queen. She dies and then the workers slowly die off. This can take 4-6 weeks.
Again, the key is to treat the entire area, and the larger area you treat, the longer it will take for the ants to re-invade.
And, as always, be sure to read and follow the label before using any pesticide.