Some early 1990 (maybe some '91s had them) horn buttons are prone to breaking due to a poor design and/or manufacturing defects. Later buttons were redesigned to reduce the chance of them malfunctioning. Like a lot of plastic part designs, the horn buttons worked pretty well for a while.

Instructions for removing the horn buttons can be found  here: Horn Button Replacement Instructions

There were three different designs.

1. The original has two legs with hooked projections at the bottom that are supposed to retain the button. The legs either break or the plastic relaxes enough that the hook will no longer retain the button and it pops out.
    
2. The second design was nothing more than fishing line installed on the part to keep the part from popping out if the hooks failed. Below are instructions I wrote on how to install the fishing line.
    
3. The latest and final design added two additional retaining hooks. These buttons will not fit into the older style housings.

The 90-91 horn button is not unique to Reattas, they were used on Riviera, Olds, and other full size Buicks. Some colors are still available new.

The fishing line fix was an interim fix until they changed the mold. Later designs had two additional hooks that greatly reduced the likelihood of the buttons coming out. Sometimes you can salvage a broken one by using fishing line.

Disconnect the battery and wait 10 minutes for any residual charge to dissipate before working around an airbag. Better safe than sorry.

Going from memory there are 2 screws, (maybe four), in the bottom side of the wheel. Remove those T-30 Torx bit screws , (a 1/4" drive stubby ratchet will make the job easier), and the center part of the wheel comes off exposing the horn buttons and the air bag.  Then remove the 2 screws holding the horn buttons on either side of the air bag. I remember something about a spring clip, but you will see what you have to do when the cover is off the wheel.