Install new wiring
This is the retrofit wiring loom that will connect the amplifier to subwoofers and power. I added explanation where each cable connects.
Now just lay the wiring in place. It should be pretty straight forward as you already removed all trims that can get in a way.
To run the cable between read and front doors, you need to undo few plastic clips and slightly open a black plastic cable covering. It's a bit tricky to undo these clips, but this allows to run your new cables with the existing wiring loom without the risk of getting them snapped in the future.
The cover looks slightly different on the other side, but idea is the same.
Remove original cable subwoofer cable and connect to into a blue adapter (it will carry signal to the front door speakers). Other blue connector goes into the subwoofer.
Now connect the ground and positive cables.
The ground/earth brown wire goes under 10mm nut.
Red positive wire connects under 15mm nut inside the battery's fuse box.
Connect the amplifier. On the bottom of the amplifier there is a small switch with two positions - 1 and 2. According to the BMW manual it should be set to position 1.
At this point you may want to temporary re-connect battery's negative terminal and ensure that the amplifier and speakers are working properly.
OK, now it's time replace front doors speakers and install tweeters.