Yeah that's almost it.
You would run the wire from the power source (with a fuse) out to your lights and the best place to connect it would be at the end of the strip where you have the most power loss.
When you reduce the load on the first wire the voltage will come up. For the power the thicker the wire the better.
I think a lot of lamp cord is 18 gauge if you can find something 16 gauge it would be better.
Keep in mind the Gage of the wire isn't the only Factor the shorter you can keep your runs of wire the better.
Now that you have the voltmeter you can try a few things out and see what's going on. You can also use it to confirm your positive and negative before you make your connections.