You should have a volt-ohm meter to test the system, you can buy them cheap at Radio Shack or Sears.
Take the Voltmeter, check at the positive and negative terminals to determine battery voltage.
Use the negative post as your ground, disconnect the horns, have an assistant push the horn pad and check at the power wire of the horns (the power wire is the one that ISN'T brown). It should be close to battery voltage. If it is, it's not a relay problem.
Do the same test using the brown wire as your ground, if the test is showing a lot less voltage, you probably have a bad ground wire.
Another possiblity is a poor set of horns. Are the horns you installed from a reputable source, and do they look like the originals? There is also usually an adjustment screw on the horns, it may help to try adjusting them.
I can try looking up the wiring circuit if you need it.
The relay is probably in the rear section of the fusebox, behind the fuses.