The way DC-powered controller works is as this: it’s powered by a low-voltage (7.5VDC to 12VDC) adapter, and it has a built-in voltage booster to generate a high impulse voltage — the impulse voltage will energize the solenoid, then it lowers the voltage to input voltage to provide holding current.
Other than it needs to be powered by a DC adapter, it works the same way as AC-powered controller. If you are based in US or Canada, your package will include a 7.5VDC adapter. Otherwise, you need to find a DC adapter yourself — 9V and 12V are both quite common.