だ
is, am, are (casual)
Noun / な-adjective + だ
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だ is the casual version of です: 学生だ, "(I'm) a student". Between friends it's normal, and in writing that isn't talking to a reader directly (novels, manga narration, news articles) it's the standard.
A bare だ at the end of a sentence can sound blunt or matter-of-fact, so in conversation you'll often hear it softened with よ or ね: 学生だよ. In casual questions it usually drops out: 学生? not 学生だ?
One rule to remember early: だ goes after nouns and な-adjectives only. い-adjectives don't need it, so 高い alone means "it's expensive", and 高いだ is wrong.
Register: Casual: friends and family, and the standard in writing that isn't addressed to anyone (novels, diaries, news).
Examples
明日は休みだ。
Tomorrow's a day off.
あの人は私の兄だよ。
That guy's my big brother.
今日も雨だね。
Rain again today, huh.
これは僕のかさだ。
This umbrella is mine.
彼女はまだ高校生だ。
She's still in high school.