Even in English you have cases. You know when to write "he" (nominative) and when to write "him" (accusative). And you know when to add an "s" for the genitive: "John's book". It's the same in German, except every noun has endings, not just the pronouns, and there's an additional case: the dative. The idea is that the accusative is used for the direct object or target of an action (the person or thing s.th. is done to), while the dative is used for the indirect object (the person who benefits or suffers from the action). That's fine as a rule of thumb, but in practice you cannot always derive the case that should be used from this rule. So instead, you should learn verb patterns (just like you should learn articles together with the noun, i.e. "der Tisch" instead of "Tisch"): jemandem (Dat) etwas (Akk) geben = give s.th. to s.o. jemandem (Dat) helfen = help s.o. and so on. Learners of English need to do the same, we have to memorize "to put up with s.th." ("sich mit etwas (Dat) abfinden"). You can find the patterns (there are often several, often with different nuances in meaning) in a good dictionary, e.g. Pons (http://de.pons.com/). For prepositions, you need to learn the case together with the preposition. Some prepositions take two cases ("Wechselpräposition"), here you have to distinguish between a place (dative) and a direction (accusative). A list of prepositions for the various cases is e.g. here: http://www.mein-deutschbuch.de/lernen.php?menu_id=175#praeposition

Mastering "case" is essential to developing the ability to think like a German. The following link gives a fairly good answer to your question: http://marathonsprachen.com/mich-or-mir-accusative-vs-dative/