Many advise boiling up a pot of water and carefully pour it directly onto the ants nest to kill the insects and destroy the nest structure. While this method is effective on smaller colonies (you will need a lot of water for a larger one, especially as ants are likely to disappear deeper into the ground), it is also a surefire way to damage your lawn, too. It is for this reason that experts advise against it also to get rid of weeds.
Expect weakened roots, soil that's been eroded of nutrients, and a garden more prone to diseases, too.