The supreme court watches the actions of the president to make sure he is acting according to what document?

The Supreme Court does not watch the actions of the President. 
I mean, the Justices may read the morning paper out of personal
curiosity, just like millions of other Americans do, but their job does
not require or consist of keeping an eye on the President.  Or on
anybody else.

The Supreme Court is a court.  That means that they come into the
office every day and wait for cases to be brought to them ... two people
who have an argument that they can't settle, and it comes all the way to
the Supreme Court and still hasn't been settled. 

THEN, the Supreme Court listens to the opinions of both sides, and then
makes the final decision of which one will get their way.  The court makes
its decision BASED ON THE US CONSTITUTION.

The court can't say anything, even if they see a lot wrong stuff going on
right in front of their eyes, until the case is brought to them.

Once the Supreme Court makes their decision, that's IT.  They're supreme,
and nobody can argue about it any more, even if they don't like the decision.