Greenland is huge, but a very hostile place so most of the population live along the south coast, if the population was compliant the US could control it with minimal forces. However the reaction to Trumps scheme by Greenlanders has been extremely hostile, and Denmark has also given an emphatic no. So the US would likely have to take it by force, you would think this would be no more than a formality for them, that they would just have to turn up. But I don't think it's so easy, pretty much any practical route either by air or sea would require them to cross into Canadian territory, given Canada's stance in supporting Denmark's position, they would likely deny the US permission to cross their borders, if the US attempted to ignored this it would bring them into potential conflict with not only Denmark but Canada as well. This scenario would risk the lives and safety of US servicemen and I would expect Trump's military advisors to strongly argue against it. I think military force is very unlikely (but not impossible) as I don't think Trump wants a war (they're expensive!). There is nothing the US could gain in Greenland that they don't already have access to, so Trump must have some other motive, I suspect he knows the whole thing is a none starter, but he thinks there's some domestic political mileage in making a noise about it. He'll likely get some minor concession from the Danes, probably a mineral rights deal that he could probably get anyway, and claim it as major diplomatic victory.