The switch is part of a switch assembly as pictured:
There is no "horn ring," like in older vehicles back in the 70s and earlier. The switches are all wired and pass through the clockspring or "spiral cable." You should disconnect the battery and wait 10-minutes before attempting to remove the air bag to access the switch panels. There's not much you can do with them other than replace the switch assembly. If you sprayed electronic contact cleaner into it, you'd probably damage the plastic finisher. If you have a lot of patience and are careful, you could try taking the switch apart to clean it, but be prepared to replace the switch if you should break it even more.