Perhaps you are having trouble because you don't understand cases? This may help;
Die Frau gibt dem Mann den Hund ihres Vaters - The woman gives her father's dog to the man
Die Frau (subject of the sentence is in the nominative) Question to ask: Who or what?" Who or what gives the man the dog belonging to her father?
Answer: Die Frau So die Frau is nominative in this sentence
"ihres Vaters" - "of her father" Question to ask: "Whose?" Whose dog does the woman give to the man?
Answer: Der Vater So der Vater is genitive in this sentence
"dem Mann" - "to the man" (indirect object) Question to ask: "(To) Whom?" To whom does the woman give the dog belonging to her father?
Answer: Der Mann So der Mann is dative in this sentence
"den Hund" - "the dog" (direct object) Question to ask: "Who or what?" Who or what (thing) belonging her father does the woman give to the man?
Answer: Der Hund So der Hund is accusative in this sentence
This question/answer scheme is what German children do to learn the cases, and it works because they typically already know how to say the sentence correctly, just not how the grammatical structure is called. It doesn't really work that well coming from English, because there is no real equivalent to the question words wer/wen/wem/wessen in (modern) English.