• We use one of after each, every, any, another.

EXAMPLE: Each one of these apples is rotten.
EXAMPLE: Every one of the rooms was infested with cockroaches.

• Every one [two words] is an expression of quantity. It can be used about any person or thing and is always used with an of.

EXAMPLE: Every one of the residents in this neighbourhood owns their own home.

• Everyone [one word] is an indefinite pronoun. It is only used about people and can never be followed by of.

EXAMPLE: Everyone, except me, has taken their bath.

• Any is a determiner. Any one [two words] is used to refer to each one or all students of the class.

EXAMPLE: Any one who sleeps in class will be sent home.

• Anyone [one word] used is a pronoun, and it refers to any person in the world.

EXAMPLE: Anyone who still believes the world is flat should think again.

• Another is a determiner. Another one refers to an additional person.

EXAMPLE: Look! Another ostrich burying its head in the sand. / You can have another one joined your group.