You'll need the Arduino IDE, and also some knowledge of how to read and write Arduino code.
To program the watch itself, you'll need an FTDI cable or FTDI Friend. This will connect your computer to the watch. If you're using an FTDI cable or anything other than the Friend, you'll also need some extra long header to press-fit.
Simply place a 6-pin extra long header into the FTDI connector and slip the other end into the top of the watch PCB, to match this photo. Be sure to have a battery in the watch, as it does need to be powered while programming!
Rename the folder to Watch (check that the renamed folder contains the Watch.cpp and Watch.h files) and install into the arduinosketches/libraries folder. For information how to use and install libraries, see our tutorial!
Restart the IDE
When programming, select Lilypad Arduino w/ ATmega328 as the "board" type