'Another' is just 'an' and 'other' written as one word.
So 'another' simply means 'one other'.
If you know how to use 'a' / 'an', you should know how to use 'another'.
We use 'an+other' for singular, countable indefinite nouns:
For all other nouns, we use just say 'other':
the other book/that other book/my other book (definite)
other books/some other books (plural)
other information (indefinite)