there are courses that you can go on which will teach you how to dispatched quickly and cleanly - often using the broom handle method. Or you could look at this and learn how to do this method:-
http://www.chat.allotment-garden.org/index.php?topic=8581.0Or you could use a sharp axe like I do or buy a chicken dispatcher in which you put the neck in and pull the handle down.
If it is a chick then placing it's neck over a sharp edge such as a metal fence and then pressing on it's neck is clean and quick.
The vets is another option or you could find somebody nearby who is able to do it.
Personally I feel that every chicken keeper should know how to do the deed in case of emergencies but I realise that not everybody feels able to do so. The main thing is to do it in a caring calm manner and to do it as quick as possible (it will seem like hours especially if you don't get it right first time but really it is over in seconds).
Remember the chicken will still flap around for a while afterwards but this is just the nerves and the bird really is dead.
Hope this helps
Just going to pop this over to the hen house as you may get more answers in that section