Check the obvious first, remove the bulb, and with a piece of wire place it directly onto the battery to ensure it actually works, if it does turn your attention to the bulbholder.
Ensure the bulbholder bottom contact is actually clean and in contact with the bottom of the bulb, then look for internal corrosion inside the bulb holder. Clean thoroughly and insert the bulb, operate the indicators, if they still do not work, run a lead from the battery negative terminal to the body of the bulb, if it now works it is an earth fault.
If not it is a supply fault, begin be checking the supply to the lamp unit, using a tester, place one lead onto the bottom contact, and the other to the metal body, if the multi meter flicks you have a supply to the unit. If it does not work, trace and identify the wiring back to the multi plug, backprobe this on either side to see if you have a supply, if you have a supply to one side, but not the lamp side, it is most likely corrosion in the connector.
Failing this it is a matter of tracing the supply back through the wiring.