This was originally a reply to a post on Google Plus but I thought it would also be useful for everyone. Using ‘other’ is difficult for some people because of the level of specificity (knowing if something is special to the topic of conversation) much like ‘a’, ‘an’ and ‘the’. Here are the basic uses.
The other: a specific singular or uncountable thing.
“Don’t buy the red jacket! Buy the other one.”
A different jacket both speakers understand.
The others: a specific countable group of things.
“If we are going to go out tonight we should invite the others.”
A group of people in the same friendship group.
Other: unspecific countable or uncountable things.
“Let’s talk to other people to see what they think.”
Another: one unspecific thing.
“I have one car already but I want another for my wife.”
A car, maybe any car.