Try to think of it this way: Essentially, the word "another" is just like saying "an other" or "a other" so you are referring to a different "other." For this reason, it just depends on what you are trying to say in a sentence.
This is a little confusing, so I will give you some examples:
1)
Speaker 1: Can you bring my glass from the table?
Speaker 2: You mean this one?
Speaker 1: No, the other one.
2)
My phone broke today, but I can't afford to buy another one.
3) Buying a car:
This car is ugly. I prefer the other one. ---- (this refers to a specific "other" car they have already seen)
4) (Same scenario, but using a general "other")
This car is ugly. Let's look for another one. (This means they will look for a different one they have not seen yet)