I read that this board allowed for electrical isolation from the Arduino board only if it has its own 5V power source. Also, since many cables come in 8 wire configurations, I thought that I could move the VCC (5V) and the ground lines to an external power source.
My thinking was to break open a wall wart and connect it to a 3 pronged plug, which includes a ground. I'm not completely sure about wiring here because the relay board requires a VCC and a ground wire and the wall wart typically has just the 2 AC plugs.
I also thought that I would use a USB cable or a phone type jack and cable but I don't know if they would carry enough current to do the switching. perhaps some other cable would be better.
Well that specific relay board you linked to is a solid-state relay board designed to switch higher voltage AC loads on and off via it's output connections. Being that is uses SSRs as it's switching elements they already have opto isolation internal to the small back SSRs on the board, so I see no safety benefit or reason you should try and power the relay board with an independent +5vdc power source. Just complete the dotted red line connection to the arduino's shield 5V pin and be done with it and ditch the external DC power supply.
PS: Here is a E-bay listing for the same board which down the page has a partial schematic drawing (of a single channel) showing the logic and use of the DC power, ground, and signal input wiring.
Thank you for answering. OK so if I stick with a standard setup, how about using standard cables like phone, USB style computer or some other style cables? I would like to stay away from D style connector. I guess that I will need 10 lines for 8 channels.
Sure, assuming we aren't talking particular long cable runs (say a couple of feet or less) you should be free to use any cabling you want as we are talking low voltage low current on the arduino side. Now the wiring you use on the switching high voltage AC should be selected for proper voltage and current rating for the service you are using it in.