OK, now at least we know what you're talking about.
They are compatible in the way that you can directly connect the Arduino output to the relay module's input. Arduino's logic is 5 V, and the module needs 2.5 to 20 V input to drive the relay. So that's OK.
The Arduino needs at least 6 V input (7 V recommended), but the circuit works at 5 V, and that 5 V is also available on the power connector, at the bottom of the picture.
Connect this 5V and the ground next to it to the relay module's power connector, and up to 8 of the digital I/O's shown at the top to the relay module's logic inputs and you're in business.
vicatcu explains that the Arduino can also be powered from the USB input, and that's true. But the relay module will draw up to 160 mA, and that may be more than your USB port will supply. The Arduino itself also needs around 50 mA.
edit 2012-07-09, re jippie's comment
The Arduino Uno's LDO voltage regulator can supply 800 mA, which should be sufficient for Arduino + relay module, together about 200 mA. At 6 V in the LDO will dissipate 200 mW, and that's no problem, but at 15 V in that becomes 2 W, and that may be too much for the NCP1117's thermal protection. After all this is an SMT device. So it's advisable to use an as low as possible input voltage, or use a separate 5 V wall wart to power the relay module.