The first thing to do is actually check if the contacts inside are working. Hook up your horn to +12v on one side and -12v on the other (or 6v if its a 6 volt horn). Touch a wrench or something metal to large screw/nut on the back. If it sticks the contact points are working and you just have to make some adjustments to get the horn working again.
So if it still doesn't work you have to open it up. Drill out the rivets from the back and crack it open. Be careful not to damage the paper gaskets when you open it. Inside you will see the contact points. Its kind of difficult to clean them in the tight area but a piece of very fine sandpaper and a spray of electrical contact cleaner will do it. You can tests the contacts with a voltmeter or just hook it up and see if it has magnetism now.