Now if you're replacing a switch you need a new one. Or you can disassemble and clean/re-lubricate the switch.

Or in my case you can disassemble the switch by releasing the 2 tabs on each side (purple set). Retrieve the broken keycap piece from inside and reassemble the switch.

Now with the switch ready to be soldered back onto the board you can take your solder, flux and soldering iron, insert the switch back through the front of the keyboard and re-solder the two contacts to the board.