Now you've determined eight separate useful button inputs, it's time to connect the wiring. Clip yourself 15cm lengths of wire to attach to the controller. I would recommend using coloured wire if possible as you can colour code each button input pair. You want to have a coloured wire connected on group A matched to the same coloured wire(s) on group B. This way you can just connect each coloured wire pair to the switches later on to make life a bit easier. You can also mark or tag the wire but I would strongly recommend labelling them in some fashion so you can make the correct connections later.
I've found the best method is to pre-tin each wire and all the contacts on the controller with some solder then fuse them together with a little heat from your iron. Once you've connected all the wires, connect the controller to a computer and test each input in notepad by touching the end of each wire pair together. When you touch the ends of each pair, a key press should be registered. If not, check you haven't bridged any of the contacts or connected the wiring incorrectly.