Some

Some is used to show an indefinite quantity, the exact number is not important. It is used in affirmative statements, for example:
- I have some pencils.
- She wants some coffee.

Some is also in questions, but only when you think the answer wil be "Yes". For example:
- Do you have some paper? (You hoping that he answer will be "Yes")
- Would you like some french fries? ( You expecting that  the anwer will be "Yes")

Any is used in negative statements. For example:
- I don't have any money.
- There aren't any taxis near here.

Any

Any is mostly used in questions, especially when we expect the answer to be "No". for example:
- Do you have any paper? (You expecting that the answer will be "No")
- Is there any time to go to the doctor's? ( You will  think there probably isn't time).

Some and any are often used like articles for plural nouns. A/an is used for singular countable nouns, and some/any can be used for plural noun, countable or uncountable. For example:
I have a newspaper, some newspapers, and some money.
"A newspaper" is a singular countable noun so uses a, "newspapers" is a plural countable nouns so uses some, and money is an uncountable noun so also uses some.