You destroy their will to live.
I drenched a colony with water using a hose, destroying what you could see of it that was above ground. Spending an hour or so just torturing them with the hose. I waited a couple hours, and checked on their progress as the ants worked tirelessly to rebuild their colony, and to move their larvae from the yard back into a newly built home for them. So I drenched them again, but this time for 10 minutes or so, making sure there larvae were floating around the yard surrounding the colony.
Then I dragged a container of roundup, and sprayed the ants that were clinging to the blades of the grass, along with their precious larvae. I didn't want to kill the grass though, so I drenched them some more with water after I had sprayed them with the roundup.
This kills the ant colony. The larvae were dead, and the surviving ant's will to live was no more.