Another is general. It is singular. It can be used as an adjective or a pronoun.
Another girl arrived at 3:00.
A guitar string broke yesterday. Another just broke.
Other is specific. It could be singular or plural, depending on the noun it occurs with. It could be a pronoun.
The other teacher was absent.
The other teachers were absent.
The other was fine.
The others were fine.
Others were waiting in the basement to yell, "Surprise!"