Nominative is used for subjects and accusative for direct objects. In “I bit the dog” or “the dog bit me”, “I” is nominative whereas “me” is accusative.

Context. "Mein guter Freund" works in the context "he is my good friend". "Meinen guten Freund" works in the context "I like my good friend". You don't actually learn all those grammar rules as such (what the heck is "accusative" anyway), you just pick all this up by actually using the language.

Similarly "Meines guten Freundes" works in the context of "the house of my good friend" and "Meinem guten Freund" works in the context of "I offered a beer to my good friend".