How exactly do you hook up the power wire? Can I clip it to the same power wire I'm using for the radio itself?

Yes, the ground as well. Just make sure to use the constant power wire going to the D3 and not the switched power wire or the BT unit will lose memory every time you turn the car off.

So clip the yellow and black wire from the Bluetooth to the yellow wire on the radio?

no the yellow goes with yellow and black with black, your radio harness should have a black wire that is the ground.