What is the correct way to use the word girl's or girls'?

The spelling girl's is the singular possessive, referring to one girl.

e.g. The girl's dress is blue.

The spelling girls' (apostrophe after the S) is the plural possessive, referring to more than one girl.

e.g. The girls' coats are hung in the left closet, and the boys' coats in the right closet.