Horn doesn't work 1996 Buick Riviera

Is the horn relay sticking, or the pad on the steering wheel ?

under the front side wheel well, driver side.you have to take off the plastic wheel rim, it is near the light.

I had to go to a salvage yard and purchase an air bag (which include the horn contacts) to repair my horn. The wiper washer could be a list of things. Does your fluid run out on the ground? - broken washer hose? Listen by your lower right front fender behind the wheel and have someone push your washer lever and see if you can hear the pump running. If not, could be a pump motor (check with a test light after pulling the inner fender) or the multi-function lever in the steering column.

Did you pull the steering wheel off the shaft? If not, you won't be able to tell anything. Sounds like the cable going through has been worn through/broken. Likely wore through until it touched something, which set it "off" but still intact, then your tugging pulled it enough to completely break what little was still intact. Should be a very simple wire splice once the steering wheel is off (that's the hard part).

the buttons are still available from a buick dealer. i bought some last year

Your ground for your horn button in the steering wheel is stuck in the on position and will require dissassembly.

Typical scenario of the horn pad needing to be replaced at the steering wheel, may have to search the wrecking yards for a replacement or take the pad off and try to discover what part of it is bad and try to repair what you have.
Some folks have added a button useing the same twop wires that control the horn pad, thus eliminating the need to find a replacement horn pad in the proper color etc. a hole drilled into the dash and the button installed makes it a lot easier and cheaper and yiou still have a horn.
Every once in a while the horn relay is the culprit but mostly it is the horn pad, be careful of the air bag deploying...disconnect the air bag fuse before doing any work on the electrical inside the car.

The contact point is in the steering wheel. You may need to remove airbag by disconnecting battery and removing the screws on backside of the steering wheel then a wire. The horn will be underneath the airbag. The horn contact will be a plastic insulator and a spring. Check here to see for broken parts. Good luck.

many of them have a removable cover if the horn is part of the airbag.... dealer part only

keep the steering wheel in one spot, do not rotate,  check horn by pressing pad in different areas.  If it is intermittent then horn pad is concern.  If it works well trying slowly turning steering wheel while pressing horn pad if there is a point in turning the wheel where horn becomes inop, then the common fault is the horn contact ring inside of the steering column