The sprinklers work on 24v. You don't get this from the board, in fact you don't want to power anything external from the board. That's why you are using relays. The omni will just operate the relays, use them to power anything you want.
A relay works by switching a common lead, from a NC closed lead to a NO lead. So if you want to STOP something from receiving power, you would connect the main power to the common and the NC to the device. So when the relay is activated it switches from the NC to the NO stopping power from getting to the device. If you want to OPERATE a device (as a sprinkler), connect the DEVICES power supply (24v in this case) to the common and the device to the NO. So in a normal state the device will not be powered, when the relay is activated it sends the power to the NO and on to the device. This can be reversed if you want the device to work when the relay is not energized but it's rare to do that.
Your sprinkler system should have come with a power transformer. That needs to be connected to all eight of the commons (if you have eight zones of course), then relay number 1's NO will connect to the solenoid for zone 1 on the positive connection. relay 2 to zone 2 etc. All the commons from all eight solenoids will be connected together and back to the common of the power transformer.
So when complete, all you are doing is putting a switch on the positive side of all the solenoids.