Each other and one another are reciprocal pronouns. They both talk about each member of a group doing the same action to the other members of the group.
When you want to talk about two people in a group use each other.
When you want to talk about more than two people use one another.
- Adam and Eve were looking at each other.
(Adam looked at Eve/Eve looked at Adam) - Mary and Joseph gave each other presents at Christmas.
(Mary gave Joseph a present/Joseph gave Mary a present) - John, Paul, George and Ringo looked at one another’s hair.
- Her three children spent the afternoon kicking the ball to one another.
Each other and one another are both singular.
Common mistakes with pronouns.