'Another' is just the two words AN and OTHER written as one word.
An + other = another
1. We use the indefinite article 'a' or 'an' for a single, countable nouns. For example:
A book
A student
An apple
When we add the word 'other' to these phrases, it becomes 'another':
I read a book in the Twilight series, and now I'm going to read another.
I met a student from Argentina last week, and then I met another one.
This apple is dirty. Can I have another apple, please?
2. We use 'other' for plural nouns (other people, other countries, other years)
We use 'other' for uncountable nouns (other information, other accommodation)
We use other for singular nouns after determiners which are not 'an', such as possessives (my, your) and demonstratives (this, that). For example:
another friend/my other friend
another bus/ that other bus
Remember - AN + OTHER = another. Es tan facil.