the relay board, like all relay boards has 3 separate voltages.
the output of the relays can be anything. they are completely isolated from the input, so no need to discuss them.
the relay has a label, in this case it is SRD-12VDC
this means that the coil inside of the relay is 12 volts DC.
that is the second voltage you need to be concerened aobut.
and this one is REQUIRED to be on a separate power supply. this 12VDC does not come from the Arduino.
the power supply has to be sized to be able to deliver enough power for all the relays to be on at one time.
now, the 3rd voltage.
the tiny squares near each relay that have 3 legs, are the transistors that send power to the coil
the larger squares are the opto isolators that signal the transistors. these opto isolators are what the Arduino drives.
an opto isolator can be thought of as an LED, if you can drive an LED, you can drive the opto.
the opto isolator should get power exactly like an LED, use a resistor to current limit the power.
I cannot read the label on the opto, it might be an AC/DC opto which means that there is no + or - that needs particular attention. so, if you connect your common to the ground for the opto's, then you feed each one with a 5v output from your pin, with the resistor to limit current.
that means. Arduino ground to the common pin
a wire from your output pin, to a resistor (330 ohm to 1k ohm) and the other side of that resistor the relay pin.
use the BLINK sketch and select your Arduino pin in that to the relay high, then low.
you should hear it click each time.
if you connect the common to the Arduino 5V, then you bring any one pin to ground (with a resistor in-line) and that will turn the opto to the ON state and the relay will click.
for the large relay boards it is prefered that you feed the common with 5 volts, then use the pins to bring to ground.
the 8 channels,
If you use a resistor selected for 20mA, and used arduino ground to the common.
your Arduino board would have to output 160mA if they were all high. this is called SOURCE
The Arduino PIN is the source of the current.
if you connect the Arudino 5v to the common and use a resisistor for 20mA for each signal line, then the Arduino would SINK the 160mA. the pins would bring that to ground.
the Arduino UNO is listed as being able to SOURCE up to 200mA from the all the output pins combined.
the UNO is listed as being able to SINK up to 400mA from all the output pins combined.
That is why it is preferred to put the 5V to common and use a resistor between each pin on the relay board and your pins on the Arduino.