You will want to download the Arduino IDE from their website. I believe 1.6.3 is the current version, though you might consider downloading an older version, 1.0.6 instead. I have heard of issues for cloned hardware on the latest version.
Plug your Arduino Mega board into your computer via the USB cable (likely a USB B to USB A cable is used, which should have come with your printer).
Open up the folder with the provided files, there should be a file called Marlin, Marlin.ino, or Marlin.pde. When you click to open the file, the Arduino IDE should open along with all of the related files in the same folder as the Marlin file.
Under Configuration or something similar in the Arduino IDE, you need to set your board type as Mega or Mega 2560 and the port your control board is plugged into should be visible in another sub-menu (normally like Port 3 or Port 4...varies).
Assuming no further changes are needed under the Configuration.h tab, you should then be able to hit the upload button which will compile and upload the code to your Arduino.
