You said “Change directory name of firmware to mainArduino” — this shouldn’t be necessary. When you check out the OpenSprinkler firmware code, it should exist in a folder, for example, called OpenSprinkler, and this should be placed inside the Arduino\libraries folder. Basically the firmware code folder structure should look like this:
Arduino\libraries\OpenSprinkler\a bunch of .h and .cpp files
Arduino\libraries\OpenSprinkler\examples\mainArduino\mainArduino.ino
Assuming you set it up correctly, start Arduino, and go to File -> Examples -> OpenSprinkler, click on mainArduino. Then compile.