Below, you will find a picture of one end of the harness. This end features a relay and a couple of wires.
The yellow wire shall be connected to +12 volts. It should be connected either directly to the positive terminal of the battery or to the main circuit in the fusebox (which usually comes directly from the battery and is protected by a large fuse).
The black wire shall be grounded. It can be connected to the negative terminal of the battery or directly to the chassis, preferably at one of the many ground points under the hood.
And next, you will find the other end of the harness, which features two wires with bullet connectors (one male, one female) and one wire with a male spade connector. You'll also find the inverter, which has two wires with bullet connectors (one male, one female) coming out of one side and two sets of wires with plastic male connectors coming out of the other side. Finally, you'll find the bulb along with some female plastic connectors.
The red wire with the white stripe that has the male spade connector is the wire used to trigger the relay. Whenever +12 volts is supplied to this wire, the lamps will be turned on. A female wire tap connector ("Scotchlok") that the male spade connector can connect to is included in the kit. It can be used to tap into a circuit.
The wires with bullet connectors coming from the relay obviously connect to the wires with bullet connectors coming from the inverter. Brown goes with black and red goes with white. The alternating bullet connectors will not allow you to connect these incorrectly.
Only one of the male plastic connectors coming out of the other side of the inverter will be used. Other applications use two bulbs per side.
The female plastic connector should be installed onto the bulb only after the bulbs has been mounted inside the headlamp assembly and the wires have been routed. It is MUCH easier to route the tiny wires than to do so with the bulky plastic connectors attached. Once the connectors are installed, they can not be easily removed.
Obviously, there is also another set of wires with bullet connectors in the wiring harness for the other headlamp. However, the wire colors are the same, so I didn't feel that it was necessary to include more pictures.
If any of this is unclear, feel free to request clarification. I hope that this is sufficient for now. I'm sure that some members will provide detailed accounts of their installs, including details on the various options for triggering the relay.