As long as you have a new head unit and not a stock. Power usually is 4 gauge and comes from the battery.

What he said, you need to run power from battery, ground to chassis and a set of RCA cables with a remote turn on wire from the head unit to the bass link. You can also use speaker level inputs, but RCA is best

Power needs to be run DIRECTLY from the battery? OR can I just combine it where my head unit gets its power from the yellow hot wire behind my HU? If not, do I have to route all the way from the battery all the way back to the sub?

Yes power needs to come directly from battery. Make sure you use a fuseable link (fuse holder or circuit breaker) of appropriate amperage.
Ground needs to be as short as possible.
Make sure you strip the paint where you are grounding, needs to be metal to metal. and make sure ground is tight and secure, can not be loose.

So do I have to run a power wire all the way up to the battery under the hood and place the wire on the positive terminal or is there an easier and closer alternative? I'm just not the biggest fan of having wires running around all over the place.

Yes, running power wire in a 370z is easy. Take the cover off the battery compartent, there is a growmet there you can go through. Make sure youdo not damage the wire when running it. You must go to Battery with an amp connection.

Thanks for clearing that up. I didnt know if it was a MUST or not. As for the wire, what's the smallest "reliable" wire I can use?

For that tube, a true 8 AWG kit would be fine.

I would run a 4 Ga just in case you decide to upgrade to a more powewrfull amp later.