In '88, the alarm did not have a remote. It armed when you locked the car with the key, and disarmed when you unlocked the car with the key. If it goes off, the owner's manual has the instructions. I think you just need to lock and unlock a door (with the key) to turn the alarm off.
1988 560SL Black/Palomino
1988 300SEL Black Pearl/Burgandy
1984 500SEC Anthracite Grey/Palomino