Tie ground of arduino to ground of supply. Put resistor in series with base of NPN transistor (1k is good), emitter to ground, collector to the pin you need to drive low. Drive base high to turn on.
Or use an N-channel MOSFET.
If you need isolation (ie, you can't connect the grounds) use an optocoupler (but with a normal output, not triac output) or relay.
Note what aarg said - computer power supplies normally only want you to manipulate one pin to turn them on.