How to control a motor if it is supplied power via an external power supply?

BROWN=GND
RED=POWER (+5V) (can be up to 6V but generally not necessary)
ORANGE = SIGNAL (PWM)

There is only one wire and it seems to be for power.

That isn't a true statement is it ?
"A WIRE" is a single conductor
The "product" (servo) (who calls a servo a "product" anyway ?) has a ribbon cable with THREE conductors. (see above)
As you can see from the information above two of the wires are for power and the third is for input signal.
Normally , I would never say this but in your case, after reading your question, I think I should:
The signal wire needs to be referenced to the GND wire. so while you can connect GND and Power to your PC, the GND & SIGNAL must go to your uController . ALSO, in case you are not aware , the "product" is controlled with a PWM signal . (not analog)

If you asked this question, I think it is safe to say you have not used one of these "products" before so do you know how to use the "product" ?