My husband told me this remedy earlier today after mowing the lawn and noticed the rather large ant hill on our lawn, he decided he was going to get rid of them the way his grandparents do.  

Note: While this may seem harsh on both the ants and your lawn, this won't hurt your lawn nearly as much as the ants.  Grass will begin to grow normally in a matter of time.  

What You Need:

A Large Pot (the kind you cook pasta in)
Water
Dish soap (the natural dish soap will work, but I recommend using liquid.)
Salt

Instructions

Fill the pot with as much water as you feel comfortable carrying around after it's boiled.  Add about 1/4 cup of salt and the same amount of dish soap into the water.  Bring it to a boil.  If you wish, stir it counter-clockwise as a way of showing your ill content for the little buggers.  Mind you, considering this is basically homemade napalm, I think they'd get your pretty done with them.

You're going to want to do this at least two times in a row. The point is to penetrate the hill and kill the queen.  If you kill her, the rest of the surviving ants will die within 3-4 days.  The soap will stick and suffocate them, and the salt is poisonous.  The water has to be boiling, as it will penetrate the hill faster, and cook a lot of the ants.

While this may seem cruel, note that this is a very quick death, and there isn't really another way to get rid of ants once they begin to destroy your lawn.

A couple of more things that I have tried,

Digging out the centre of the hill, can be messy and has the potential to be painful as the ants go after who is digging up their home. If you successfully move the queen to another area, the other ants will follow. Fill the hole with other soil, and re-seed. I've done this successfully.
I have read this other idea somewhere, I think it was in a book, not here but someone can correct me if I'm wrong.  There was this man who was having an ant problem in his home.  He had a conversation with the ants, telling them that he was unhappy with them living in his house, and could they please leave, because, he felt he had no other options but to bring out the ant poison if they didn't move on.  He did this with no malice or anger, just a point of fact, and this was supposed to have worked.
I didn't do this with ants, but it has worked with the crows.  They were sitting in the trees outside my front door, having a cawing festival everytime I walked outside.  The noise was driving me crazy.  I told one in particular that if she (yes....she) didn't stop, I would get my son's bb gun and use it on her.  I understood the need to communicate but it was too much for me.  They do their sessions down the street now, but that one usually hangs around now, and we talk back and forth.  Ok, the neighbor's probably think I'm crazy..........