не + Verb

Negation in Russian is straightforward. Here are the basic rules for beginners, followed by some advanced nuances you will encounter later.

1. Basic Placement
Place не immediately before the verb you want to negate. It is written as a separate word, except for verbs that do not exist without не (e.g., ненавидеть - to hate).
Example: Я не знаю (I don't know).

2. Negating Sentences with Two Verbs
When a sentence has a conjugated verb and an infinitive, the placement of не changes the meaning entirely. Place it before the conjugated verb to negate the whole idea, or before the infinitive to negate only that specific action.
Examples: Я не хочу пить (I don't want to drink). Я хочу не пить (I want to not drink).

3. Double Negatives
In Russian, you must use не even if the sentence contains negative words like никто (nobody) or никогда (never). If a negative pronoun (but not a negative adverb) is used with a preposition, the preposition splits the pronoun into three separate words.
Examples: Я никогда не сплю (I never sleep). Я ни с кем не говорю (I am not talking to anyone).

4. Existential Negation
When negating existence in the present tense, use the word нет (or its colloquial equivalent нету). Historically, нет is a contraction of не есть ту (where ту is an old demonstrative meaning 'here', which is the direct ancestor of the modern word тут). The logical subject takes the Genitive case. In the past and future, нет becomes the impersonal не было (which is always neuter singular, regardless of the logical subject's gender or number) and не будет, which also force the logical subject into the Genitive case.
Example: У меня нет машины (I don't have a car).

--- Advanced Nuances ---

5. Genitive of Negation
When you negate a verb, the direct object often changes from the Accusative to the Genitive case, especially with abstract objects. Additionally, the particle ни (not a single) forces the use of the Genitive case for direct objects, but it does not override other cases governed by verbs.
Examples: Я не вижу выхода (I don't see a way out). Он не сказал ни слова (He didn't say a word).

6. Aspect in Negation
To become confident with Russian negation, note that the imperfective aspect is typically used to express that an action simply did not happen. The perfective aspect indicates that an anticipated result did not happen.

7. Negative Imperatives
When telling someone not to do something, use не with the imperfective imperative as the default for all negative commands, including polite and gentle requests (e.g., Не делай этого!). Using не with the perfective imperative is used as a warning against an accidental, undesired result (e.g., Осторожно, не упади!).

8. Impersonal Prohibitions
For strict, impersonal, or public prohibitions, use не + imperfective infinitive. You will often see this on signs.
Example: Не курить! (No smoking!).