There are two electrical circuits for your horns.
Circuit one energizes the coil of your relay when you press the horn button. The other connects the battery to thehorns them selves.
If you have someone press the horn button while you listen to the relay (put a screwdriver against the relay and the other end to your ear), you will hear a click as the contact moves. If you do not hear the click, then the problem is either a blown fuse or with the circuit from the horn button to the relay. If it does click, then the problem is between the relay and the horn.
To troubleshoot further:
1-Disconnect your battery.
2-Unplug your relay and use your continuity tester to verify that your socket has:
a-Continuity between the battery and pins 30 and 86 of the socket. Check the other 3 pins to verify no continuity.
b-Continuity between pin 87 and ground (with the horns in the circuit, the resistance will be greater than 0 ohms) and no continuity between any of the other pins.
c-Press the horn button and verify that you have continuity between ground and pin 85. When you release the horn button, the continuity should go away.
3-Check your relay to verify:
a-That you have coninuity only between pins 30 and 87a; and
b-pins 85 and 86.
c-There should be no continuity between any of the other pins.
Report your findings
Also, this thread may be of assistance to you as well:
Need help rewiring my new horn relay connector. - Page 2 - Pelican Parts Technical BBS