Does it mean a broken wire if a doorbell transformer works, but there is little-to-no voltage at the switch?
Switch Wire Continuity
Checking the continuity of the wires between the switch and the chime is easy, finding the break (if there is one) is hard.  To check the continuity...

Turn the breaker that supplies the doorbell transformer off, and verify power is off with a non-contact voltage tester.
Disconnect the wires in the chime that go to one of the switches (don't forget how they were connected, mark them if you have to).
Twist the wires you just disconnected together.
Go to the doorbell button and remove it from the wall.
Using a multimeter in continuity mode (or the lowest resistance setting), touch the leads to the switch terminals.

If the wires are good, you'll hear an audible tone and/or get a reading close to 0. If there is a break in the wire, you'll get a reading of infinity.  If the wires are broken, inspect them along the entire length for damage. If you can't find the break or can't access the wires, replacement might be easier.
Switch Continuity
While you're checking continuity, it may be worth it to check the continuity of the switches themselves.

With the power to the transformer off, disconnect the switch from the circuit.
Measure the continuity in the default OPEN position.
Then press the button to close the switch, and take a reading in the CLOSED position.

When the switch is OPEN, you should get an infinite or very high reading.  when the switch is CLOSED, you should get a low nearly 0 reading.