You need an Arduino UNO board, I used a Seeeduino v2.21 here - it did the job very nicely back in the day, but a couple of new features have been added to the code and so it doesn't fit on anymore. Genuine UNOs have very slightly more space for programs.
Upload the source code to the arduino. Look at this fine guide courtesy of Adafruit for help.
Because it changes regularly, I have not attached a copy of the code itself to this step, but the very most recent version can be downloaded in a bundle from the polargraph code repository.
You should save the code file into a new folder inside your arduino sketch folder. Give the new folder the same name as the source code file. So if the file is called polargraph_server_a1.ino, you should create a new folder called polargraph_server_a1 and save the file into it.
It also uses Adafruit's AFMotor library and Mike McCauley's Accelstepper libraries. Please use the copy of Accelstepper that is in the zip file - the newest versions of it have a few fixes in them that the polargraph code isn't yet updated for.
The AFMotor library files should be put into a folder called AFMotor inside your Arduino/libraries/ folder.
The Accelstepper library files should be put into a folder called AccelStepper inside your Arduino/libraries/ folder.
Once they are moved, your arduino installation directory should look something like the second image on this page.
Of course the source code is also available in the code repository - https://github.com/euphy/polargraph_server_a1 - should you want the very most recent version.
Once you do that, you should confirm that it is working properly - use the serial monitor on the board, set to 57600 baud to make sure that it is issuing "READY" every couple of seconds (see the third image).