This is a very difficult one and there are many answers but I have found a kettle full of boiling water poured directly into the nest usually works. Make a hole into the nest and pour away!

Ants are very important parts of the garden eco-system and shouldn't really be killed unless it's absolutely necessary. Of course they can set up home in the worst possible place and that's when they can become problematic. There are all sorts of noxious chemicals that kill ants but also take out spiders and a whole array of beneficial invertebrate life-forms, so I would urge you not to use anything like that.

There's a new-ish nematode available called 'No Ants' that effectively disperses ants from lawns, as well as from plant beds etc:

http://www.ecocharlie.co.uk/grow-your-own/pest-and-disease-control/nemasys-no-ants.html

The ants will not tolerate the presence of the nematodes so basically break up their own colony.