In order to learn how to produce PCBs, I designed a backpack for the popular standard HD44780 LCDs. It is similar to the previous backpack which I had assembled on a strip-board. Python and Arduino sketches can be found on my Arduino project pages.
The PCB was manufactured at fritzing.org. Dimensions of the PCB are approx. 22 x 42 mm. Schematics can be downloaded here.