〜ません
doesn't, won't (polite)
Verb ます-stem + ません
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Swap ます for ません and the verb becomes negative: 食べません, "(I) don't eat" or "(I) won't eat". Like ます, it covers both habits and plans: お酒は飲みません, "I don't drink"; 明日は行きません, "I'm not going tomorrow".
You'll also hear the plain negative plus です, 食べないです, which means the same and is very common in conversation. Both are accepted here.
ません is for verbs. After a noun, "isn't" is じゃありません (学生じゃありません), and "there isn't" is ありません. It's easy to mix these up at first because they all end the same way.
Register: Polite. 〜ないです means the same and is common in conversation.
Examples
私はお酒を飲みません。
I don't drink alcohol.
日曜日は働きません。
I don't work on Sundays.
朝ご飯は食べません。
I don't eat breakfast.
明日は学校に来ません。
I'm not coming to school tomorrow.
テレビはあまり見ません。
I don't watch much TV.