The diagram above assumes that you do not want the horn to work when the car is off.
First, you need to find a +12v power source somewhere in your dash. If you want to horn to only work when the car is on, find a wire that turns on when you turn your car on (the wire that turns your stereo on will work). If you want the horn to work when the car is off, you need to find a wire in your dash that is a constant +12v (you can also use a wire that goes to your stereo).
Now that you have found thw +12v wire, hook that to one of the connectors on the switch, hook the other connector on the switch to the #86 plug on the relay.
Hook the #85 plug on the relay to a good chassis ground (just about metal part of your car will work).
Hook the #30 plug on the relay to the positive terminal on your battery. It is a good idea to put a fuse inline here, 5amp should be fine.
Hook #87 on the relay up the positive wire on the horn. Hook the negative wire on the horn to a good chassis ground.
Now when you press the button, it will activiate the relay, which will turn on the horn.
Parts list from Radio Shack:
12v Relay, PN 275-226, $6.29
Inline fuse holder, PN 270-1213, $2.39
5 amp fuse, PN 270-1079, $1.49
Crimp-on Quick Connects, PN 64-3058, $1.69
Momentary Switch, PN 275-618 (or similer, pick one you like), $2.29
15ft or so of 16gauge wire, about $5
Total price is about $20.
If you want to go ultra cheap (but not too safe) you can leave out the relay and hook the wire from the switch directly to the +12v on the horn, then just ground the -12v on the horn to the chassis. I don't recommend doing it that way, but it will work.