When the light is out, first replace the bulb with
one you know will light. With the new bulb in the socket
turn on the switch. If light doesn't go on, check the
fuse box or circuit breaker in the basement. If fuses are
all good or the breakers are not tripped, the problem
is probably the switch.
Purchase a switch. If the light can be turned on from
two different wall switches buy a "2-way switch". If only
one switch turns on light, buy a "regular switch".
Remove fuse or flip circuit breaker to off, usually
found in the basement.
Unscrew and remove the face plate on the wall switch.
Unscrew the top and bottom mounting screws and pull
switch box out.
Loosen the terminal screws on the side or end of the
switch and remove switch.
Connect a new switch to the wires. Hook wires in a
clockwise direction around screws so wires will wrap
around screw when it is tightened. The black wire shouldgo to the brass colored screw and the white wire to the
silvery colored screw.
Reassemble the switch, doing the above steps in
reverse order.
Purchase a switch. If the light can be turned on from
two different wall switches buy a "2-way switch". If only
one switch turns on light, buy a "regular switch". 
Remove fuse or flip circuit breaker to off, usually
found in the basement. 
Unscrew and remove the face plate on the wall switch.
Unscrew the top and bottom mounting screws and pull
switch box out. 
Loosen the terminal screws on the side or end of the
switch and remove switch. 
Connect a new switch to the wires. Hook wires in a
clockwise direction around screws so wires will wrap
around screw when it is tightened. The black wire shouldgo to the brass colored screw and the white wire to the
silvery colored screw. 
Reassemble the switch, doing the above steps in
reverse order.