Yes, you can test the cord with a hand-held meter for continuity. That isn't a bad thing to do occasionally, even measuring resistance of the three conductors. That process may turn up a problem within the assembly.
What you will find in your cord is that the three conductors are wrapped in paper. This is a measure to add longevity to the cord assembly. Peel off the paper and you will find the three conductors are sheathed in the appropriate color sheathing, green, white, and black. Install the cord's wires as recommended above--line voltage (black) to a brass terminal, neutral (white) to a silver terminal, and ground (green) to the ground terminal. After assembly, you can test for continuity (or resistance), again. Test between terminals to make sure there is not a stray wire strand or other issue.
Tips: Make sure you have the jacket of the cord assembly long enough to be secured by your new cord end. Some of these cord retrofit ends have less than optimal retaining clamps so that I sometimes use a piece of shrink wrap that envelops the bottom of the jacket entry and the cord. The shrink wrap makes the connection between the two more durable.
