I've gotten the code more or less in a shareable state. Still not perfect I'm sure, but good enough for now.

The layout for USB keyboarding is defined here:

https://github.com/AnthonyDiGirolamo/teensy-thumb-keyboard/blob/master/firmware/LayoutThumbKeyboard.h#L109

If you don't need a USB keyboard and are rolling your own hardware project then you can focus on this layout:

https://github.com/AnthonyDiGirolamo/teensy-thumb-keyboard/blob/master/firmware/LayoutThumbKeyboard.h#L74

There are three layers defined: base, shift, and Fn layers.

USB can be disabled by commenting out define USE_TEENSY_USB_KEYBOARD. 

All the keyboardy goodness is handled by the keyboard_update(); function called from inside the standard arduino loop().

If you don't need the keys to behave like a keyboard you can gut most of that example and just use key_matrix.update(); The KeyboardMatrix class handles reading the button states.

An alternative firmware option for a pure USB keyboard would be to run the excellent https://github.com/qmk/qmk_firmware.