Need help on Arduino and relay control
That manufacturer's web page is rather confusing but here's the relevant part of the circuit. It shows that JD-VCC must be supplied with power for the relay to operate, at the moment it sounds like you only have VCC connected that would operate the LED but the relay after the optoisolator would not have any power available.



Then moving onto the board diagram there is a jumper marked VCC on one side and JD-VCC down the bottom-right. If you don't require a seperate power supply you should be able to connect them together to get the relay to operate. 

It has a flyback diode in place so I'd say the only time you'd need a seperate supply for the relay is if your main supply can't supply around 4 x 100mA = 400mA of current for the coils. The particular part you linked to mentions a 5V relay which will be the coil voltage so if you do need a seperate supply only use 5V on JD-VCC, the voltage you are switching doesn't affect that.