This is a totally new subject for our school team, since we are mostly programmers, so your help will be really appreciated.
HobbyKing, which sells Arduinos and is a great source for motors and controllers, has an instructable on this at http://www.instructables.com/id/ESC-Programming-on-Arduino-Hobbyking-ESC/
I found another on the OpenROV site, at http://community.openrov.com/forum/topics/how-do-i-activate-electric-speed-controller-with-arduino
Did you actually try googling "arduino electronic speed control" before coming here?
As the controller and motor are from the same vendor, they can help you with specific questions.
That motor controller is designed to emulate a servo motor. So it takes a servo-motor signal: Ground Power PPM signal
The Arduino servo library will drive the PPM signal. Power and ground for the controller need to come from a separate power supply. The Arduino can't power it.