It sounds like maybe you aren't using the meter properly? You should be set on a resistance scale. If you have different scales, you should be on Rx1 or 200 depending on your meter.

If you have a digital meter and you're in the right mode, you should usually read something like OL on the display to indicate an "open lead". If you short the probes together, you should read 0. If you have an analog meter, your needle should be full left scale with the leads apart, and full right scale with the probes shorted together.

That cleared up, you should be reading resistance (it will be very low). The best way to check is to put your black lead on the engine block and touch the red lead to the wire connected to the glow plug. You should read just shy of 1 ohm.

If you read a hard 0, you have a short in your wiring harness or a shorted glow plug. If you read OL, you have an open circuit. If you read high resistance (anything above 1) you have a failed or failing glow plug. Generally if you really do have a short in your system, you'll take out that strip fuse (that's why it's there).