Dud Light
Using a voltmeter is really very simple, especially if it is the digital kind. Insert the one probes into each of the cables and see what teh meter says. If you get a minus figure, then you are reversed polarised. Swap the probes around. You should get a reading of at least 12 volts and hopefully a little more, maybe 12.4 - 12.6. Dop not let the probes touch or you will blow the fuse.
I would suggest that you check the inside of the bult holder with the meter to see if you have power to the bulb. If not, follow the cable back, paying attention to any joints, and sooner or later, you will get a reading. You will either have a cable break or a very dirty connection.
Do you take you vehicle wading at all? Verdigris, which is a green deposit found on copper which has been exposed to the damp, will act as an excellent power inhibitor. It is also quite possible that what looks like a sound connection is actually corroded to a point where the power cannot get through.
If your bulb holder is a bayonet fitting, check for rust around the inside rim. This will kill the earth side, although given that the turn signal works, it doesnto sound like an earthing fault. I would suspect a dirty, corroded or broken connector at the bulb holder end.
Let me know how you get on.