It is marked on a passport with a green stamp showing the text ENTRY GRANTED, the current in-game date (or November 23rd, 1982 in the latest beta), and a shield icon also featured in the Ministry of Admission seals.
One should be approved to enter Arstotzka if they meet the requirements of immigration protocol stated in the Basic Rules section of the rulebook (i.e. valid papers). Failure to do so will lead to a citation.
If a passport has been mistakenly stamped with entry approval, the inspector may stamp entry denial on the approval stamp to deny entry. The reverse is not applicable, however.