です and だ

です joins a topic to what it is: X は Y です means "X is Y". It is polite and fits almost any situation. Its plain form is だ.

• 私は学生です。
  Watashi wa gakusei desu.
  I'm a student.
• 田中さんは先生です。
  Tanaka-san wa sensei desu.
  Mr. Tanaka is a teacher.
• そうです。
  Sō desu.
  That's right.

です doesn't change for person or number: it covers "am", "is" and "are". When the topic is clear, it is left out: 学生です "I'm a student." The final u of です is barely heard: "dess".

Forms

じゃ is the spoken short form of では. ではありません is the most formal and suits writing; じゃないです is the most common in conversation.

• 私は学生じゃないです。
  Watashi wa gakusei ja nai desu.
  I'm not a student.
• 昨日は日曜日でした。
  Kinō wa nichiyōbi deshita.
  Yesterday was Sunday.
• 昔、ここは公園だった。
  Mukashi, koko wa kōen datta.
  This used to be a park.

Plain だ

だ is used with friends and family, and in writing such as diaries and novels. On its own at the end of a sentence it can sound blunt, so casual speech often softens it with よ or ね, or leaves it off: 雨だよ "It's raining", そうだね "That's right." In casual questions it is dropped: 学生？ "Are you a student?"

With adjectives

な-adjectives work like nouns: 静かです, 静かだ, 静かでした. い-adjectives are different: the past and negative are part of the adjective itself, and です is added only to make it polite. They never take だ.

Verbs don't take です; they have their own polite form, the ます form.