What's the difference between the German cases?

The case system in English is not really used anymore so it's a common for difficulty for native English learners of German to get their heads round it! In German there are 4 cases which change articles (the/a/my/his/her etc.) and adjective endings depending on the word's function or role in a sentence. The nominative case is for the grammatical subject of a sentence i.e. the thing that does the verb. The accusative case is for the grammatical direct object of a sentence i.e. the thing that has the verb directly done to it. The dative case is for an indirect object (normally demonstrated in English with "to"). Finally the genitive case which in English we demonstrate with possession as "'s". See all 4 cases demonstrated in the sentence below:
Ich(I - subject - nom) gebe (give - verb) den Fußball (football - direct object - ACC) meines Bruders (my brother's - GEN) meiner Schwester (to my sister - indirect object - DAT). --- I give my brother's football to my sister.