Easy: “Another” is just the indefinite article “a” (“an” before a vowel) + “other”. The only reason for your confusion is that Spanish has a unique rule where the indefinite article is always omitted before “otro/a”. 1. Just form the sentence without “other” and without “another”. 2. Notice whether or not you need “a” (or “an”). If yes, then use “another”. If no, use “other”. Comments: 1. If we use “the”, then obviously we don’t use “a” or “an”. 2. If the word is plural, then obviously we don’t use “a” or “an”. 3. If the word is uncountable (a mass noun), then obviously we don’t use “a” or “an”.

Yes there is a subtle difference between the two words depending on the context when the word is needed. Other is to be used when talking about a person or thing that is different from someone or something already mentioned. "My other phone is not working" Another is to be used when talking about someone or something which is the same, that has already been mentioned. In addition... Your drinking a beer, your beer is finished. "Can I please order another beer please". "My table needs one more chair, can I have another chair for my table please". "Today I do not have time, I will go to the market on another day". The two words will become more easier to use once you are talking, reading, listening and writing more in English. I hope it helps!