If you look on the board where the buttons are there are copper contacts in each spot. Each button uses 2 contacts for signal and ground. When ground is shorted to the signal lines, it equals a button press in-game. You should be able to see where the signal lines go to the CPU, and how the ground lines are all connected to each other.
All you have to do with your tact switches is wire individual signal and ground leads to two legs on the same side of a switch. When you press down, the switch will bridge the two signals and facilitate your button press.
You can rough up the pads with sandpaper or sand down the masking over the traces to get solder points. The ground lines don't matter where they come from as long as they are ground.
To simplify this a little, you can actually wire all of the ground lines on the switches together, and then to a single grounding point on the board. That way you can keep most of the wire mess between your switches and then just have signal lines and 1 ground line coming off the board. Otherwise you need two wires off the board for every switch.
Hope that makes sense.