Troubleshooting three way switches will involve determining whether the switch is bad or not. You can use a voltage tester to find out.
How Three Way Switches Work
A three way switch will always have power at two poles. One would be for the power
Use a non-contact voltage meter to check and see if you have power to the switch. With a three way switch you always have power to one side or the other. You should get a reading no matter whether the switch is up or down.
Make sure you have checked the bulbs before proceeding. Try the bulbs in another fixture that is working before you automatically assume it is the switch. Does the meter show that you have power to the switch? Yes, then the switch could be bad and need to be replaced. Or the wiring could be loose or corroded.
Turn the power off and take off the cover plate for the switch. Check it with the tester to make sure the power is off. Remove the screws that hold the switch into the box. Pull the switch out and examine the connections.
Are the loose or corroded? Yes, then clean them and tighten them. Turn the power back on and see if this has taken care of the problem. Yes, then it is a job well done.