To get started, remove the factory amp cover. Just grab it by both sides and gently pull/wiggle it out, it has 2 clips on the side but no screws holding it in place. The exposed amp will look like this:

Remove the 2 connectors from the bottom of the amp. Both connectors are wrapped with black electrical tape, peel it back about 5 inches to expose more of the wiring and make it simpler to splice into the wires.

The smaller wiring harness that came with the subwoofer has 6 wires with twist-on splice connectors that work kind of like Scotch-Locks, but they don't damage the insulation as much. The white plug will only have 2 connections, the power wire and the remote turn-on lead. Look for the large red wire with a white stripe on the alpine harness, that will connect to the red wire on the FAST-9999 harness. This will be a tight fit, but pull the cap off the fast harness and insert the red/white alpine wire into the slot. You have to kind of squeeze the end back together to get the cap started, but you should be able to thread it on a few turns and that is enough for the connection. It should look like this:

Do the same for the remote turn-on lead. It will be a smaller guage red wire with a yellow stripe on the Alpine harness, this will go with the blue/white wire on the fast harness. This harness is made for speaker-level inputs instead of the smaller line-level inputs. So the front speaker outputs on the black Alpine harness are what the remaining wires will plug in to. I originally tried to tap into the line level inputs on the white plug, but they didn't drive the amplifier enough to be usable. Also, the rear speaker outputs on the amp have a high-pass filter to block the bass, so they are unusable for the subwoofer output. On the black alpine harness, the purple/orange goes to the fast harness grey wire. Purple/black goes to grey/black. Yellow goes to white, yellow/red goes to white/black. When you're done, it should look like this:

Now you can connect the FAST-9999 harness to the long Bazooka cord. There is a 6 pin connector, should be self explanatory. Towards the end of the bazooka cord before the heat shrink wrap there is a ring terminal on a black wire, this is your ground. I chose to ground the amp at the lower right mounting stud for the Alpine amp. Just remove the 10mm nut and put the ring terminal on the stud and tighten it back up. This grounding point gives me no alternator whine or ground loop noise on my Abarth, but it may get noise on the 500e, YMMV.

Now, you have to hide the excess wire for the harness. I just lifted the carpet/cardboard toward the back of the car and tucked it under the plastic trim. Plenty of room under there.

Then you can route the wrapped end of the long harness to come out where the amp cover will go over it:

Install the amp cover, being careful not to pinch any wires in the fasteners. The harness can come out through the bottom of the amp cover like this:

Plug in your subwoofer and make sure everything is working. Just a suggestion, turn the BASS level on the stereo to 0 and adjust the gain on the BAZOOKA to taste. This will take some of the strain off your front speakers that aren't good at bass frequencies, and it should help keep your doors from rattling. The straps that came with the subwoofer get screwed to the floor and the subwoofer strapped in securely:

Now you have a system as good or better than the Beats system for less than 150 bucks.