(你) + 不要 + [verb phrase]
(你) + 不要 + [verb phrase] + 了
[subject] + 不要 + [noun]
不要 before a verb tells someone not to do something. As in English, the "you" is often left out.
别 means the same as 不要 and is shorter. It's what you'll hear most in speech.
With 了 at the end, it asks someone to stop something they're already doing.
请不要 is the polite form, used on signs and in requests to strangers.
Before a noun, 不要 refuses something: "I don't want it".
Before a verb with 我 as subject, 不要 sounds like a stubborn refusal: 我不要去 is "I'm not going!". To say you don't feel like doing something, use 不想.