I am trying to get my Arduino to control a relay without luck. I'm able to see the LED flashing on the relay board indicating that the relay should be throwing, but the circuit is not being closed. I'm wondering if its because the circuit on the relay is too low of a voltage? I've got a 12 volt circuit.
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.
You should power up relay board before you can control it with MCU. According to schematics, +5V (or +12V, depending on relay requirements) should be connected to JD-VCC.