"One" is being used here as a pronoun, a generic stand-in. We don't need to know what is being put over on the person for the sentence to make sense, it stands in for lots of possible things. (Any form of deception from the benign (joke or prank) to the dangerous (a con).)
Similarly, if I said "have one at the pub", most folks would know I meant "a drink", but not specifically what kind.
In the now-memetic "One does not simply walk into Mordor.", the word "one" stands in for "A person".
This usage has changed over time. The phrasing above was designed to give the sentence an archaic feel. The modern usage replaces "One" when referring to a person like this with "You", which can lead to misunderstandings but is now common. "You don't stack dirty and clean dishes together.", even when referring to the actions of a third party.
For objects, we would use "anything" more commonly these days. "No one was going to put anything over on him." However, the phrase you reference has become an idiom, so it retains the older usage.