This is a resistive analog joystick, very similar to those found on the PSP1000. These compact joysticks are different in that they have a very interesting 'slide' feeling.
For wiring this part, if you look at the device from the bottom the pin out goes
Pin 4 is the pin closest to the 2 mounting tabs found on one side of the device. When connected to an Arduino, you can expect a range of about 128 to 775 on each axis.
The rubber thumb pad is removable if you desire.
The pads are spaced by 2mm, but it is possible to get our 2.54mm headers connected with a bit of bending.