Each other and one another are normally used in the same way.
We see each other/one another everyday. (= Each of us sees the other everyday.)
They looked at each other/one another.
Both expressions have possessive forms.
They enjoy each otherīs/one anotherīs company.
"One onother" is more common when more than two people are involved. However, "each other" can be used.
The soldiers looked at one another/each other.