Each other and one another are used in the same way in modern English. One another is preferred when we are making general statements.

We see each other / one another every day. (= Each of us sees the other every day.)
They can sit for hours without talking to each other / one another.

Note that each other and one another are not usually used as subjects in a clause.

They sat for hours listening to what the other said. (NOT They sat for hours listening to what each other said.)

Each other and one another have possessive forms.

They would spend hours listening to each other’s / one another’s stories.

Words used without each other

Each other is not usually used after meet, marry and similar.

They met in 1999. (NOT They met each other in 1999.)
They married in 2004. (NOT They married each other in 2004.)

-selves and each other / one another

There is some difference between -selves and each other / one another.

Compare:

They talk to themselves for hours. (= Each of them talks to himself / herself for hours.)
They talk to each other / one another for hours. (= Each of them talks to the other.)