Another thing or person means an additional thing or person of the same type as one that already exists.
Mrs. Madrigal buttered another piece of toast...
We're going to have another baby.
You use another when you want to emphasize that an additional thing or person is different to one that already exists.
I think he's just going to deal with this problem another day...
The counsellor referred her to another therapist.
You use another at the beginning of a statement to link it to a previous statement.
Another time of great excitement for us boys was when war broke out...
Another change that Sue made was to install central heating.
You use another before a word referring to a distance, length of time, or other amount, to indicate an additional amount.
Continue down the same road for another 2 kilometres until you reach the church of Santa Maria...
He believes prices will not rise by more than another 4 per cent.
You use another in front of the name of a well-known person, place, or event to indicate that you think someone or something is just like that person, place, or event.
You may never be another Hemingway, but you can learn to write well.
You use one another to indicate that each member of a group does something to or for the other members.
...women learning to help themselves and one another...
The two countries do little trade with one another.
If you talk about one thing after another, you are referring to a series of repeated or continuous events.
They had faced one difficulty after another with bravery and dedication...
They kept going, destroying one store after another.
You use or another in expressions such as one kind or another when you do not want to be precise about which of several alternatives or possibilities you are referring to.
...family members and visiting artists of one kind or another crowding the huge kitchen...
All of these industries have at one time or another been linked to cancer.