I don't have first hand experience with the Infinity unit, but it's not really different from anything else.
First off, you're not going to get the greatest sound quality out of the factory HU, period. Your best bet is to go aftermarket. Then you can just use the sub outs on the back of the HU and run RCA cables to your amplifier.
If you're dead set on keeping the factory HU then you will need to install a line level converter. You can do this by tapping into the speaker outputs on the back of your HU. I would go with the rear outs since the speaker is going in your trunk. Then you will need to run a fused power cable(4 gauge should be enough) from your battery, through the grommet in the firewall behind the clutch, then down the drivers side of the car under the door sills, and into the trunk. It would be easy to run your remote wire from your HU in the same place at the same time. Then find a good place to put your ground(closer to the amp the better), drill a hole directly through the body of the car, sand the paint away from around the hole, and screw a bolt into it to secure your ground. Then it's just a matter of running RCA cables from your line level converter to your amp, and adjusting the gain..
Existing wiring isn't going to be sufficient to run an aftermarket sub.