Identifying USB wires
It's easy to just test the connectivity from the pins on the connector-end of the cable to the bare wires at the other end. 

Even a hardware store multimeter is good enough for this test.

Disconnect the cable at both ends. Set your meter to the ohms function. 

Touch one probe of the meter to one pin of the connector. Touch the other probe to one of the wires. If the wire is connected to the pin, you'll see (near) zero ohms. Depending on your meter you might also get a beep for continuity.

The pin assignments for the connector are readily available. Here's a picture from Wikipedia:


If your connector is a mini or micro type, those pinouts are also available from the Wikipedia article on USB.