First you need to see what you have. On the back of the Xenon light you'll have three places to plug stuff in - the upper one is for the leveling motor (requires a switch and running wires to the dash, optional), and below that you have a grey female plug and a black one. The ballast plugs into the grey one, that's obvious/easy, but the black plug might not have the male connector there. Don't forget, most of these lights are sold in Japan as "replacements" so the seller assumes the person will use the harness they already have.
a) there is no male plug on the black side, you will have to wire it up directly using waterproof connectors (cutting off the black female Xenon connector and male OEM connector completely). (Then move on to "c" below.)
b) you have the connector but not enough wire sticking out (happens a lot) then you can either follow "a" above, or use the pin connectors inside the plug to insert four new wires, then put the other ends of those wires into waterproof connectors to attach to your OEM harness. (Then move on to "c" below.)
c) you have black male connector on Xenon side and enough wire, then you'll want to cut the wires on the car side before the OEM connector, then put those wires into female waterproof connectors. Put male connectors on the headlight side of both the JDM lights and the OEM ones (if you intend to keep OEM ones ready to swap back in one day). The two black power wires on the JDM headlight should be twisted together, installed in the female waterproof connector and plugged into a single male connector from the car side. Do the same thing for the remaining two wires, one plugs into one. That way you should end up with 3 connections to make on each light. The JDM harness has 4 wires because it supplies power separately to the high beam and low beam, but you don't need them to be separate.
For the corners, same thing. Cut off OEM light socket and use connectors to join up the JDM ones. If you don't have the male side of the JDM connector, you can either cut the JDM female off and install the OEM one, or cut the whoel thing off and just use connectors.
I know I wrote this so that even a 6 year old could do it, didn't mean to dumb it down quite so much, but that's the way I need my instructions for myself. If someone says "just test the voltage on the [...]" then I'm already like "Uh ohhh..."
HEADLIGHT > black female connector > black male connector > 4 wires > 3 female waterproof connectors (2 black wires together in 1 connector) > male waterproof connectors > 3 wires from OEM harness > CAR