Electrically, a keyboard is just a grid of wires with a switch at each intersection. Pressing a key (switch) makes a connection between a single row and column. To read the keyboard, a controller energises the wires in one axis one at a time and checks each wire on the other axis for a circuit. If there is a circuit between a particular row and column then the key at that intersection is pressed (Probably, but I'll come back to that in another log).
In the picture above, pins 1 is permanently connected to pin 4 and pin 2 is permanently connected to pin 3. Pushing the switch connects all four pins. This means that I can carry the column connections through the switch, bypassing the row wiring. A solder joint across two pads connects each row to the one below it.
Although my prototype has the keys laid out in a rigid grid, this is of course not usually the case with keyboards. Keyboards generally have their rows offset and include keys of different sizes, which sometimes cross multiple rows or columns. I don't think that different sized keys are practical with my design, but I want to look at offsetting the rows at some point. As this is meant to be a thumb keyboard, not a full sized one, I think that this is an acceptable compromise.