だ／じゃない
The plain form of です and its negative and past formsmachine translation
FormationNoun／な-adjective + だ・じゃない・だった・じゃなかった
だ is the plain form of です: the sentence 学生です, said to friends, becomes 学生だ. From it you get all four forms: negative じゃない, past だった, past negative じゃなかった. じゃ is a contraction of では, so in formal writing you'll see ではない・ではなかった with exactly the same meaning.
An important note: only nouns and な-adjectives take だ. An い-adjective can end a sentence on its own — 面白いだ is wrong; the correct form is 面白い; its negative and past also conjugate by themselves: 面白くない・面白かった.
In casual conversation, だ at the end of a sentence is often dropped, especially in questions: 今日は休み？ (day off today?). But before grammar patterns you can't drop it freely: with 〜と思う you must keep だ (休みだと思う), and with ので, だ changes to な (休みなので).
Examples
今日は休みだ。
Today is a day off.
この問題は簡単じゃない。
This problem isn't simple.
昨日は雨だった。
It was rainy yesterday.