Unscrew and remove the tail of the flashlight. Remove the batteries. Unscrew the head of the flashlight and gently pull the bulb out so it doesn't break during the repair.
Insert the switch removal tool in the tail end of the barrel, leading with the end with longer pins. Slide it into the barrel until it makes contact at the head. The piece it is coming in contact with is the lower insulator. The piece has two holes in the bottom that the repair tool's prongs will fit into. Rotate the repair tool until the prongs slide into place.
Hold the barrel upright so the base of the repair tool is on a flat surface. Gently apply downward pressure until the upper insulator at the top of the barrel separates and you can remove it. Slide the barrel off the tool slowly -- the lower insulator should be resting on the top of the tool. If it isn't, tap the tool and it should fall out the bottom of the barrel.
Examine your replacement switch to make sure it is assembled properly. These come pre-assembled, but they can be damaged in shipping. Separate the lower insulator and the upper insulator of the replacement switch by putting the entire assembly on the long-pin end of switch repair tool and applying downward pressure with your fingers on the lower half of the assembly. The upper insulator should come loose so you can remove it.
Put the new lower insulator on the short-pin end of the switch repair tool. The side contact, a small metal piece, should be facing up. Push the lower insulator into the barrel of the flashlight using the switch repair tool. Slide it in until it stops nearly flush with the top of the flashlight barrel.
Connect the new upper insulator with the lower insulator by pushing its pins into the holes of the lower insulator to complete the switch replacement.
Reattach the bulb in the upper insulator. Screw the head and tail pieces into place after removing the repair tool and replacing the batteries.