Other ou Another ?

Quando usamos OTHER ou ANOTHER?

Primeira explicação:

Other is an adjective meaning 'different'.
Another expresses quantity, something extra or additional.

Exemplos:

Have the other cup of tea, not this cup.
Have another cup of tea, not just the one cup.

Segunda explicação:

These words refer to something different, remaining, or additional. They are placed before the noun. Another is used with singular nouns, other with singular or plural.

Exemplos:

Plural: There are other jobs you could try.
Singular: Where's the other packet of cereals?
Singular: Have another cup of tea.

An exception to this rule:

When you use "another day" and "other day" the meaning changes.

another day = a different and separate day usually in the future.
other day = a different day in the past.