です
is, am, are (polite)
Noun + です
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です links a topic to what it is, the way "is" or "am" does in English: 私は学生です, "I'm a student". It goes at the very end of the sentence, after the noun.
Two things surprise English speakers. First, です never changes with the subject: I am, you are and it is are all です. Second, the subject is left out whenever it's obvious, so 学生です alone is a complete sentence: "(I'm) a student."
です is the polite form, the one textbooks start with and the one to use with anyone you don't know well. Among friends it becomes だ, or disappears altogether. The final す is so light it usually sounds like "des".
Register: Polite. The default with anyone you don't know well: strangers, teachers, shop staff, colleagues.
Examples
私は学生です。
I'm a student.
これは私の本です。
This is my book.
田中さんは先生です。
Mr Tanaka is a teacher.
今日は月曜日です。
Today is Monday.
山田です。よろしくお願いします。
I'm Yamada. Nice to meet you.
駅はあそこです。
The station is over there.