There should be continuity between the. 1 turn off the power to the circuit at the main panel.

Apnt 23 Understanding 2 Wire And 3 Wire Lighting Systems
3 way switch not working on one side. In the former case you may simply have a miswiring issue. Identifying the common wires. Turn off the power at the circuit breaker remove the 3 wires from each of the switches and make sure that none. There are a pair of wires that run between the two switches. In this step you will be turning the power back on do not touch any of the wires previously removed with. Each switch powers one or the other leg at all times.
Disconnect all three wires or four if the outlet is grounded. Remove the two 3 way. Using a continuity tester check continuity between the common black terminal and each of the traveler terminals. Test a 3 way switch turn off power to the switches at the circuit breaker and using a tester make sure power is off. Three way switches work by alternating the power connection between 2 legs called travelers. How to troubleshoot an improperly wired 3 way switch step 1.
3 install the first. In the latter one of the switches has likely gone bad. There are many ways that a three way switch can be wired but usually power or the light fixture connect to the load side of the switch and traveler wires run between traveler screws on both switches. In this case the traveler wire and load wire were swapped and repairing the circuit involved switching them back. 2 turn the power back on. Now using your multimeter you are going to determine which of the three colored wires is.