Touch voltage detector to live wire to confirm it works.
Confirm no electricty around light switch cover with voltage detector.
Remove Light Switch From Wall
Unscrew and remove light switch cover.
Confirm no electricty in wires around the light switch with voltage detector.
Unscrew and remove light switch from wall.
Unscrew and remove wires from light switch (so you can fully remove light switch from wall).
Remember (or write down) which wire connected to which light switch connector screw so you can reconnect properly later.
Check Light Switch Continuity
Set voltage meter to continuity testing setting.
Touch the voltage meter probes together to confirm it reads near 0 resistance.
Turn light switch on.
Touch the voltage meter probes to the light switch screws (that wires were connected to). Near 0 resistance confirms light switch works when on.
If this does not work, you may need to buy a new light switch (but first try cleaning the light switch connection screws as in the "Clean Wall Wires" section below).
Othwerise, turn the light switch off. Confirm that voltage meter now reads open circuit.
If the light swith passes this test, then the light switch is not the problem.
Check Wall Wires Are Electrified
Make sure that the wires in the wall where the light switch was removed are separated (so they do not close a circuit on the next step).
Flip breaker back on.
Touch voltage detector to the wires in the wall. Confirm if electricity is reaching this point.
Flip breaker back off!
If there was no electricty in the wires, reconnect the light switch (to avoid lose wires) and call an electrician.
Otherwise, there may be an issue with the electricity conducting from the wall wires to the light switch.
Clean Wall Wires
Inspect the wires, if they look dirty or blackened they may need to be cleaned.
Prepare two mixtures: white vinegar with a little salt (for grittiness) and water with some baking soda (to neutralize vinegar).
Submerge wires in vinegar mixture (or wipe with mixture if submerging not practical).
Wait a few minutes (reapply often if you are only able to wipe vinegar mixture on).
Scrub/wipe the vinegar off the wires.
Submerge/wipe the baking soda mixture on the wires to neutralize the acid in the vinegar
Dry the wires.
Reconnect Light Switch
Connect the wires back to the light switch connector screw (as they were originally).