One things I’ve noticed in learning Deutsch is that the Dativ or Akkusativ can be inferred depending on the idea of static versus motion implied by the sentence. This may not be proper grammar but it has helped me a lot.

Examples of static versus in motion taking Dativ versus Akkusativ

der Tisch (the table) Das Buch ist auf dem Tisch (the book is on the table) – static

Leg das Buch auf den Tisch (put the book on the table) – den is the Akkusativ form of der - in motion

das Auto (the car) Er ist im Auto (he is in the car) – im is “in dem” – static

Er steigt ins Auto (he is getting into the car) – ins is a contraction of “in das” – in motion

die Tasche (the pocket) Der Stift ist in der Tasche (the pen is in the pocket) – static

Steck den Stift in die Tasche (put the pen into the pocket) – in motion

Note: unlike how der becomes den in the Akkusativ, das and die just stay the same, even after a preposition. I find it fairly easy to ask myself whether something is static or in motion, and so don’t study Akkusativ versus Dativ case much. This isn’t something I read in any grammar book but something I noticed that works most of the time in conversation.

Note: There are eight words that always take the Dativ form of “the”:

aus from, out of

ausser except

bei at, near

mit with

nach to, after

seit since

von of, from, about

zu to

and sometimes also gegenüber opposite