You will need the following things for the installation:

1. Gamecube
2. KunaiGC
3. Disassembly equipment
4. Soldering equipment

You need to disassemble the Gamecube (easiest way how to do that: Look at iFixits-Guide, how to do that)

Disassemble the Gamecube up to the heat sink and now stop for a second.

It's a bit tricky to get the heat sink off, since the thermal pads are most likely the original ones, that are a few years old.

First take of all the screws from the heat sink. Now turn on the GameCube for a few minutes, to heat up the CPU and GPU. This softens the thermal pads and you should be able to get the heat sink of without much force and hopefully without tearing the pads in the process.

With the KunaiGC you don't need to life any pins on the IPL.

Simply lay the QSB-Board over the IPL:

Solder every pin from the QSB to the IPL Chip - please use flux:

Before aligning the KunaiGC modchip make sure to tape the backside of the PCB to ensure there are no shorts:

Align the KunaiGC and check if it fits in a proper way:

Now you can take the assembled and programmed KunaiGC and solder it directly to the QSB:

To check the soldering you can test at this points:

Once you have checked the installation, you can reassemble the console.