"other" is used for "not this, but that" situations. "Do you want this one? No, the other one." "another" is used when talking about alternates or additional "This road is blocked. Take another one." or "These cookies were good. I want another one."

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)