Some:
is used with the plural form of nouns, and with uncountable nouns

a pen, some pens
some water (uncountable)

is used in positive sentences

There is some milk in the fridge.
I did some exercises.

is used in offers

Would you like some tea?

is used in requests

Could you give me some tea, please?

Any:
is used with the plural form of nouns, and with uncountable nouns

a pen, any pens
any water (uncountable)

is used in questions

Is there any milk in the fridge?

is used in negative sentences

There isn't any milk in the fridge.