The constitution isn't all that long and it explains how the government works in general.
Basically what is constitutional is up to the US Supreme Court to decide, so if somebody thinks the president is doing something unconstitutional they can file a lawsuit and pursue it all the way to the supreme court.
Of course, the party has to have a standing i.e. to have suffered some damage from those unconstitutional actions. Basically you can't sue on some abstract principle that doesn't affect you.
If the courts decide the president is ok that means it is ok whatever he does is in line with the constitution, if they decide he is not they can order him to stop.
The last time a lot of people disagreed with the supreme court's decision there was a civil war and the winning side amended the constitution so that the issue they fought over was settled explicitly.