Using the diagram above, you can see how the three buttons will be connected. Since all buttons need to share a common ground with the Gemma M0, but we only have one available GND pad, we'll run ground to a terminal on one button (it doesn't matter which terminal) and then connect the rest of the buttons to that terminal.
You can try this arrangement out right away with the short alligator clip leads, or use the longer arcade button quick connect wire pairs and alligator clip to male jumper wires for the greater length we'll need in the final table as shown below.
To begin, connect the terminals of each wire pair to the lugs on the buttons.
Note: on the larger, threaded button with internal LED (which we won't be using), we'll connect only to the switch lugs which come out of the grey switch box, not the LED pair set deeper into the button housing.
Next, connect the ground wires as shown here using the black short alligator clip leads.
Connect the four wires extensions (black to GND, yellow to D1, blue to D2, and white to D0) to the alligator clip leads with male pins as shown here, being careful to connect to the correct leads, not the ground sides which will remain unused.
This is how the final wiring will look.
Plug in the Gemma M0 to power, and you can test out the buttons. The built-in DotStar is an RGB LED, and it make for a pretty handy indicator light. The code will light the DotStar to the same color as the button pressed as a handy way to check that everything is wired properly. Plus, it adds a bit of a fun light show while you're playing!
Now, you can try it out on your iPad (or iPhone as shown here). Plug the Gemma M0 into the short USB cable and then into the USB-to-Lightning adapter and into the iOS device. The camera import screen may pop up, you can ignore it and hit the home button. Then launch the Notes app and press the buttons to type the keystrokes.
OK, enough anticipation, launch the Pinball Arcade game and in the settings, click the iCade button until it reads "iCade:iPad". Then, launch a table, and test out your buttons!