Any is a determiner. It suggests an indefinite quantity or number. It is used when it is not important to say how much/many we are thinking of.

• Is there any water in the bottle?
• Have you got any friends?
• Have they got any children?

Any is often used in questions and negative clauses, and in other cases where there is an idea of doubt or negation.

• Are there any witnesses?
• Do you need any help?
• I haven't got any money.
• I have hardly any food in the larder.
• You never give me any help.

Any is also common after if

• If you need any help, let me know.

Any, no, not any

Note that any alone does not have a negative meaning. It is negative only when it is used with not.

• See that you don't do any damage. (NOT See that you do any damage.)

No means the same as not any, but is more emphatic.

• He has got no friends. (More emphatic than He hasn’t got any friends.)

Any and Any of

Before a pronoun or a noun with a determiner (the, this, my, your etc.) we use any of.

• Do any of these books belong to you?
• I don't think any of us want to work tomorrow.
• She doesn't like any of my friends.

Note that when any of is followed by a plural subject, the verb can be singular or plural.

• If any of your friends is interested, let us know. (formal)
• If any of your friends are interested, let us know. (informal)

Any with singular countable nouns

Any is the plural equivalent of a/an. It is often used before plural and uncountable nouns.

• They recently bought a new car.
• Have they got any cars?

But note that any can be used before a singular countable noun with the meaning of it doesn't matter who/which/what.

• Can you recite any poem by heart?
• Do you know any cardiologist here?

With this meaning any is common in affirmative clauses as well.

• Come any day you like.
• There is some risk in any project.