Installing new dishwasher but using existing power cord
Use a multimeter set to test continuity or resistance.  Touch one probe to a prong on the plug, and the other to one to the wires. If you get a reading, it means the prong you're touching is connected to the wire you're touching.  Label the wires as you locate them.

NOTE: Do the testing with the cord not connected to anything.

Or go to the local hardware store, and pick up a new cord.