The nominative case is used to describe the subject of a sentence. The subject is the main actor in the sentence, the person who carries out an action:
Die sieben Zwerge wohnen in der Dachetage.
The seven dwarves live in the loft apartment.
Ihre Wohung ist hell und groß. Aber manchmal vermissen die Zwerge ihr altes, romantisches Haus aus dem 19. Jahrhundert.
Their apartment is bright and big. But the dwarves sometimes miss their old, romantic house from the 19th century.
Dort haben die Zwerge ihre geliebte Prinzessin, Schneewittchen, kennen gelernt.
It was there that the dwarves met their beloved princess, Snow White.
The nominative case is also used to describe predicate nouns (i.e., nouns that are on the other side of verbs such as sein, bleiben, heißen, werden, scheinen from the main subject):
Die Prinzessin ist und bleibtdie schönste Frau, die die Zwerge sich vorstellen können.
The princess is and remains the most beautiful woman that the dwarves can imagine.
Sie ist auch sehr intelligent; Schneewittchen wirdRechtsanwältin.
She is also very intelligent; Snow White is is going to be (i.e., training to be) a lawyer.
In the first example, die Prinzessin is the main subject and die schönste Frau is the predicate noun. In the second example, Schneewittchen is the main subject and Rechtsanwältin is the predicate noun.
The biggest trick to being able to use the nominative case (and all four cases, really) is to know the gender of nouns. If you don't know whether Zwerg is masculine, feminine, neuter or plural, the cases can't really fall into place.
Definite and indefinite articles in the nominative case
Articles in the nominative case (there is no equivalent of the indefinite article in the plural, since, just like in English, you can't say "a dwarves"):
das junge Paar
ein junges Paar
Following are the personal pronouns, which can replace nouns (and only exist in pronoun form for the referents: I and you), in the nominative case: