Your meter has a continuity setting that "buzzes" when the two probes are touched together (complete the circuit) correct?
If you think you have a short to ground, you find one end of each wire you need to test (such as the ECM connector if that wiring is suspect) and you simply connect one probe (does not matter which) from the meter to ground, and touch the other probe to whatever wire you want to check. If the meter buzzes, the wire is connected to ground.
If there is a short to ground (or it's a ground wire, you need to have a wiring diagram to make sure, but normally pink, orange, or those colors with a stripe are not grounds, all other colors are up in the air) the meter will buzz. You must make sure you have a good ground though. I prefer using jumper wires with alligator clips on them for the ground side, so that it frees up a hand. I also always check my meters ground by touching ground somewhere else on the vehicle, to make sure the meter works as it should.
A wiring manual diagram would help, because you can use that to determine what circuits that fuse feeds, which will help you find the components where you can test the wire at the connector.
Do not puncture the wire jacket with anything to test, that allows a path for corrosion to form. Test at the factory terminated ends (or factory splices if there are any) only.
