In an affirmative statement (not question), use some.
"She has some money." "She has some pens." (You can't use 'any' in these.)
In a negative statement, use any.
"She doesn't have any money." "She doesn't have any pens."
In questions, use "any" or "some".
"Do you have some money?" "Do you have any money?"
There are some other small differences, but this is the most important.