How do you know which case to use after German prepositions?

There are three possible cases that follow prepositions: accusative, dative or genitive. The following prepositions are followed by the accusative case: bis,durch, fuer, gegen, ohne, um Example- Ich will ohne dich nicht zum Party gehen. The following prepositons are followed by the dative: aus, ausser, bei gegenueber, mit, nach ,seit, von, zu Example- Er ging jeden Tag zu der (zur) Schule. The following prepositons are followed by the gentivie case: anstatt, trotz, waehrend, wegen Example- Trotz des schlechten Wetters ging er draussen. The following verbs take both accusative and dative: an, auf, hinter, in, neben, ueber, unter, vor, zwischen -The prepositions are followed by the accusative case if movement is involved. Example- Er legte den Stift auf den Tisch. -Yet when the phrase does not involve movement the prepositions are followed by the dative case: Example- Der Stift lag auf dem Tisch.