You didn't mention the year, so I'm assuming it's a pre-90 with the extra white switch up on the brake pedal. As I recall, there is a screw on side of the bracket facing the passenger side. Remove that screw and the mounting bracket will slide over towards the passenger side and come right out. Much easier than trying to get the switch out of the bracket.
The switch itself can be take apart by carefully pressing the little tabs in and pulling it apart. There is a spring in there so don't loose that. Clean out the dried up grease, clean the contacts, and put a little silicon grease on everything and button it back up.
If you have an auto, this switch also tells the tranny computer to disengage the torque converter lockup, btw.