If you have OpenSprinkler DC — please do NOT use 24VAC power supply. The instructions are very clear about never using 24VAC power supply on OpenSprinkler DC. Because of the way OpenSprinkler DC works, you should only use a low-voltage DC power supply (the one that comes with the controller is 7.5VDC 1AMP, and you can use your own, anywhere from 5VDC to 12VDC is fine).
In theory you can also power the controller using a USB cable connected to a USB adapter like phone charger. Though the 5V from USB charger is a bit low, it is often sufficient to drive solenoid valves.
About wiring valves: this is fairly standard: each valve has 2 wires. One wire from each valve should come together and that goes to the COM (common) terminal (there are two COM ports, either one is fine). The other wire from each valves goes to an individual station port (1 through 8). So if you have 5 valves, there should be 1 COMMON wire, and 5 individual zone wires.