Well, I did find some old horn pieces so I can show you a bit of the stuff:
http://i1154.photobucket.com/albums/p535/JonGoodman/IMG_8648.jpgYou will see the contact part, the horn button retainer and the horn button here.
The horn relay looks generally like this:
https://www.classicparts.com/1947-54-Horn-Relay/productinfo/53-311/(not a plug for Classic Parts. Just a quick picture I found).
Since your horn is going to take a decent amount of current to honk, you need a relay so your horn button won't be switching all that current. The relay is an electromagnetic switch that takes an impulse from your horn button, pulls a switch to the "on" position and sends the heavy current to your horn. You'll normally have 3 terminals. As I recall an input terminal, an output terminal and a terminal for the horn button. The input terminal takes in a larger current via a heavier wire and the output terminal sends via a heavier wire that current to your horn. The horn button uses a small amount of current to activate the electromagnet which pulls the circuit closed (inside the relay).
Jon
