How to: Connecting 4-pin Joystick to Arduino board
If the link that Mark Smith provided is correct, that is a “dual-axis mini xy joystick module PSP 2-Axis Analog Thumb Joystick Module Thumb Joystick for Arduino”, with (as other comments suggested) pins labeled on back of board as GND, X, Y, VCC.  

To use it, attach GND to Arduino ground; connect each of X and Y to analog inputs, like A0 ... A7; connect VCC to (typically) 5 V.  Then read results on your analog input lines.

Note, it makes sense to test the device using a DVM beforehand.  Measure resistance from GND to VCC to find out overall resistance, so you can decide if 5 V is appropriate or if you should use a lower voltage.  (For example, if overall resistance is several thousand ohms, 5 V is ok; if only a few hundred, add one or two thousand ohms in series and take analog readings using a 1.1 V reference instead of 5 V reference.)  Also measure resistance from GND to X as you move the thumb control, and from GND to Y.