If you're using the SimpleRobot demo, then you would use the instance of the Joystick class to retrieve the value of the Joystick.
Code:
// assuming that there is an instance of the Joystick class called 'stick' in the current scope
float some_X = stick.GetX();
float some_Y = stick.GetY();
However, if you glance at how the joystick values are translated to motor speed (see RobotDrive.cpp), its probably not the stick values you want to look at, you'll want to look at the motor values -- which is harder if you use their RobotDrive class, which doesn't allow you to easily access the motor values unless you create the speed controller classes outside the RobotDrive class and pass it in through the constructor of RobotDrive. For this reason, we chose to write our own RobotDrive-like class.
Reading the WPILib source code is the best way to understand how things work underneath.