The general shape of the process
Vietnam's system for foreign teachers is built around the work permit as the anchor document. Once a school agrees to sponsor you, they typically file for the permit with your legalised degree, criminal record check, health certificate and passport copies. Only once that's approved does a longer-term visa or temporary residence card usually follow.
None of this is something you can complete alone from a hotel room in Hanoi. It runs through the employer's HR or an agent they use, and provincial offices can interpret national rules slightly differently, which is part of why identical-looking job ads sometimes have different document asks.
