So lets begin... The below is a pic of some of the tools I liek to use, they are not all necessary, but you will need wire strippers, a NES Security bit, a small phillips screwdriver, a power, and a soldering iron. optionally below I have a set of "helping hands" for soldering, and a magnetic dish for my screws (both items can be purchased at harbor freight for next to nothing and really come in handy for all your mods). You will also of course need a 3.5mm Stereo jack and 3 wires about 5-6 inches long. Wires should always be sealed with heat shrink or electric tape. I salvage all my wire from SNES and NES controllers that I have scrapped for DMG button swaps.
Once your work area is ready, you can start taking apart the cart. Remove the 4 security screw with your bit as seen in the image below.
Once all 4 are removed you can lift from the bottom and the cart should come easily apart. You may set the top half aside for now and pick up your phillips head and remove the small screws as seen in the image below.
You may now easily pull out the PCB and prepare for soldering. You will need to strip the tips of your 3 wires on both sides. Just like pro sounding your Gameboy, you will want to make the exposed portion or wire sorter on the side that your soldering to the PCB (helps avoid and cross talk since you cant easily Heat shrink them). Don't forget to tin the pics on both ends of each wire.
Connect the wires (in any order at this point) to your stereo jack. After you solder them in place slide on some small pieces of heat shrink tubing.
Now that your jack is all prepped and ready to be connected to the PCB, It's time to do just that. So grab your PCB and use the image below to connect the 3 wires where they need to go.
Once connected your wires should be connected like this.
before you put your cart back together you will need to drill your hole for your jack. Grab the top half of your cart shell and drill your hole in the upper right hand side (im sure the left is just fine too) as seen in the image below.
you can now set the 2 halves of the cart side to side and put your PCB pack into place. See the pic below for an example of how to run your wires.
You can now put your cart back together, and rock out on your SNES with a little more custom flair.
HOPE THIS WAS HELPFUL!!! ENJOY!