Double-check that you're removing the switch that you intend to!

Remove the solder from the three pins of the old switch.

If you have one, a desoldering gun is the easiest tool to use. Otherwise, you could use a handheld desoldering pump or some desoldering braid along with a soldering iron.

Pull the old switch out of its holes. You may need to loosen any remaining drops of solder with a soldering iron while doing this.