To me, the easiest way is if the object that you're talking about is having an action done TO it or an action is done FOR it. For example- Der Mann gibt der Frau den Apfel. - Translated- The man gives the women the Apple. The apple is being GIVEN and the women is what the apple is being given TO. Hope this helps!
EDIT- Thus, the Apple being given means it would be in AKKUSATIV and the women receiving it would in DATIV.