This Instructable builds on some great work at http://www.instructables.com/id/EXU9BO166NEQHO8XFU (Draw Electronic Schematics with CadSoft EAGLE) and http://www.instructables.com/id/EZ3WN1QUKYES9J5X48 (Turn your Eagle schematic into a PCB). Eagle is free.
Step 1: Designing the schematic
Step 2: Place all the components
The wonderful thing about having boards like this made compared with building homemade boards is you don't have to worry about trying to optimise the autorouter for a single layer. Just run the autorouter once and it defaults to double layer mode and it always produces a 100% design automatically within a few seconds. Even with components a lot denser than this board Eagle always autoroutes the whole board.