Troubleshooting of lamp which refuses to work after bulb change
Grab your non-contact voltage tester (you do have a non-contact voltage tester, don't you?).
Turn on the switch.
Move the tester near the sockets (don't jam it in the socket, it's non-contact, remember).

If there is voltage at the fixture, inspect the sockets to make sure the contacts are in the proper position, and clear of debris (remember to turn off the breaker, Before sticking your fingers in the socket).  Sometimes the contact inside the socket can get bent, and prevents the bulb from properly making contact when screwed into the socket.
If no bells and whistles go off.

Turn off the breaker.
Carefully remove the fixture from the ceiling.
Insure that all connections are secure, and properly connected.
Inspect the fixture for signs of arcing, or other damage.
Turn the breaker and switch on.
Move the non-contact tester near the wires feeding the fixture.

If bells and whistles go off, replace the fixture (or have it done by an electrician, if you are not comfortable doing it yourself).  If there are still no bells and whistles, you'll have to move to the switch to make sure it is functioning properly.

Turn off the breaker.
Carefully remove the switch from the wall.
Insure that all connections are secure, and properly connected.
Inspect the switch for signs of arcing, or other damage.
Turn the breaker on, and the switch off.
Move the non-contact tester near the wires attached to the switch.
Turn the switch on.
Move the non-contact tester near the wires attached to the switch.

If there is voltage coming into the switch, but not going out of the switch (when it's on).  Replace the switch (or have it done by an electrician, if you are not comfortable doing it yourself). If there is no voltage at the switch in either position, call an electrician to trace the circuit further.
WARNING
If at anytime during the procedure you see sparks, the breaker will not reset, or you just don't feel comfortable doing any of the steps, please contact an electrician.