Well, there are a variety of ways I can think of to do that. It might require occupying something as small as the pumping port in the south (forget the name after all these years). You can deal with locals as the Brits did with the Saudis for years. Or you can simply deny it to them.
Trump is saying ‘take the oil.’ He certainly wants us to consider that as taking a significant cut for ourselves and leaving the locals with, at most, less loot than what they’ve used to. The locals would be motivated to NOT work with us, as they wouldn’t be getting their usual cut. They will be motivated to resist that, especially since there’s not much else worth much there. Controlling the oil port wouldn’t do it as the oil is well north of there. They’d just not send any to the port. They might even move it and sell it through neighboring countries to spite us. You have to defend everything from the wells through the whole length of the pipelines to the port facility (which is a ways inland up a river) and all the way out through the gulf until out of reach of their Shiite allies in Tehran. You either need to provide security yourself or set up the equivalent of another Saddam as a puppet to do it for you. If the latter is even possible there today it would still require a lot of US support forces. There is no off the cuff implementation possible for Trump’s off the cuff claim.