The Nominative Case: the dictionary form
Кто? Что? — the unmarked form you find in the dictionary, the subject of the sentence, and the form that follows a zero copula.
The Nominative is the default case: the form a noun has when nothing is being done to it, the form printed in the dictionary, and the starting point from which every other case is best understood. It answers two questions — кто? for people and animals, что? for everything else. When you look a word up, you are looking up its nominative.
It has two main jobs. First, the subject of a verb: Студе́нт чита́ет, Маши́на стои́т у до́ма. Second, the predicate after the invisible 'is': Он студе́нт, Москва́ — го́род, Пого́да хоро́шая. Note that both halves of that second pattern stay in the nominative in the present tense. In the past and the future the predicate noun usually shifts into the Instrumental instead — Он был врачо́м, Она́ бу́дет врачо́м — but that is a later refinement.
The nominative is also what you use with э́то when pointing (Э́то кни́га), after вот (Вот дом), in isolation, and in direct address: Ма́ма, иди́ сюда́. Russian has no separate vocative case, so calling somebody is simply their nominative — or, very informally, a truncated form like Мам! or Пап!
The nominative plural is where the noun first changes shape: -ы/-и for most masculine and feminine nouns (столы́, кни́ги), -а/-я for a common group of masculines (дом → дома́, го́род → города́, лес → леса́), and -а for neuters (окно́ → о́кна). Spelling rules interfere: after г, к, х, ж, ш, щ, ч you write -и, never -ы, so кни́ги but not кни́гы. The full picture is under noun-plural.
Examples
- Студе́нт чита́ет кни́гу. The student is reading a book. — студе́нт is the subject, in the nominative Listen in Russian: Slow in Russian: Студе́нт чита́ет кни́гу.
- Москва́ — большо́й го́род. Moscow is a big city. — both nouns are in the nominative Listen in Russian: Slow in Russian: Москва́ — большо́й го́род.
- Кто э́то? — Э́то мой брат. Who is this? — This is my brother. Listen in Russian: Slow in Russian: Кто э́то? — Э́то мой брат.
- Учи́тель говори́т, студе́нты слуша́ют. The teacher is speaking, the students are listening. Listen in Russian: Slow in Russian: Учи́тель говори́т, студе́нты слуша́ют.
- Ма́ма, иди́ сюда́! Mum, come here! — address uses the plain nominative Listen in Russian: Slow in Russian: Ма́ма, иди́ сюда́!
- Дома́ ста́рые, а о́кна но́вые. The houses are old, but the windows are new. Listen in Russian: Slow in Russian: Дома́ ста́рые, а о́кна но́вые.