Chinese has two everyday ways to say "not". 不 (bù) is for habits, plans, wishes and how things are. 没有 (méiyǒu) is for things that did not happen or have not happened yet, and it is the only way to say "don't have".
Use 不 for what you do or don't do in general, and for what you will or won't do. Use 没有 when an action did not happen in the past, or has not happened so far.
Both go straight before the verb. Compare 我不去学校 (I'm not going to school) with 我没有去学校 (I didn't go to school).
不 is always used with 是, and normally with adjectives such as 冷 or 忙 and with words like 会, 想, 认识 and 知道. This is true even when you talk about the past: 昨天不冷 means "it wasn't cold yesterday".
不 is normally said bù, but it changes to bú before a fourth-tone syllable: 不是 bú shì, 不去 bú qù, 不会 bú huì.
没有 says that something did not happen. With 还 in front, it means "not yet". In speech, 没有 before a verb is often shortened to 没.
The most common mistake is to use 不 for the past: 我昨天不去学校 is wrong for "I didn't go to school yesterday"; it sounds as if you had decided not to go. Another mistake is to add 了 to the verb after 没有. 没有 already says the action did not happen, so say 我没有吃饭, not 我没有吃饭了.
The verb 有 (to have, there is) is never used with 不. "I don't have" is always 我没有, never 我不有, and this is true for the past, present and future.
You can ask a question by putting the positive and negative forms side by side. In this pattern 不 is said lightly, with no tone. To ask whether something has happened, put 没有 at the end after 了.
To answer "no", repeat the negative with the verb: 不去 (no, I'm not going), 没有 (no, I didn't / I don't have), or 还没有 (not yet).
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