1) Check you fuses and that the other electrical equipment running on the same fuse works. I found the cheap fuses tend give me endless hassles. The better quality fuses are soldered on the end cap. The cheap ones use a spot weld principle and when you draw high current the spot weld is undone.
2) Check the horns, if you put 12V directly on it - (after disconnecting the wires) take 2 wires, each from the battery and touch the connections. do they work? if not this is most likely the problem
As a note If one of the connections is earthed you probably have a relay in the circuit.
3) Check if you have any voltage (should be 12V) when the button is pressed on the horn connection (in engine bay), i.e. those on the actual horns.
4) Check that you don't already have a relay in the circuit. if so check if the relay clicks when horn is pressed, if so check that the supply voltage is correct .
5) Remove the wire between the horn brush and the harness.( below dashboard from the cowling there should be single wire connected via bullets into the harness Earth the harness point and check if the horns work, if so you know it's the brush or horn button. if the horns do not work , the problem is not with the button but could be in the wiring , relay etc.
You can add a normal touch to make button (door bell button) under the dashboard as short term solution for a horn button problem. earth the one side and connect the other side to the harness
6) Check the horn button, the horn button has two exposed metal bits. the one connection on the bottom touches the spring brush setup and the other connection is a wire one side of the cap that touches the steering wheel and keeps the horn button in place. use your ohm meter and check that you have a zero resistance between these 2 points when you press the button.
7) Check steering connections, i.e. recently on a refurbished steering wheel I noticed that the paint was so thick that this spring did not actually touch any metal.
8) Ad a relay, critical!