How do cases work in German?

There are 4 cases in German: the nominative, accusative, dative and genitive. The nominative is used for the subject of the sentence (the thing/person doing the action). The accusative is used for direct objects (the thing/person that receives the action). So in the sentence "Er las das Buch", 'er' is the subject in the nominative case, and 'das Buch' is the direct object in the accusative case.
The dative is used for indirect objects (the thing/ person who benefits in the sentence). The genitive is used to show possession. So in the sentence, "Ich schenke dir die Blumen zum Haus meines Vaters", both "dir" and "zum Haus" are in the dative case and "meines Vaters" is in the genitive.