The nominative case is used for the subject of the sentence. The accusative case is used for the direct object in a sentence. For example,
"Der Schriftsteller schreibt einen neuen Roman."
The subject of the sentence is Schriftsteller; this noun is used, therefore, in the nominative case. "What is the author writing? - A new novel." The noun Roman is the direct object; that's why it is used in the accusative case.
Another example:
"Der Mann liest den Brief."
Der Mann is the subject (nominative); den Brief is the direct object (accusative).