Is "mladého dědečka" genitive or accusative here? From the context of the sentence, I would assume it's accusative. However, both accusative and genitive have the same endings for "dědečk" and "mladý", as far as I can see.
It is indeed accusative. Accusative singular and genitive singular have the same endings for masculine animate nouns.
How can I learn/understand the different cases? Are they explained somewhere?
At many places in fact. Our Tips and notes, Wikipedia, mluvtecesky.net and many more.