1) "another" is made up of "an" and "other". If you remember that a/an is the indefinite article, this can help you to remember that "another" is an indefinite other. "I have just eaten a sandwich but I am still hungry so I want another one." Freddie Mercury sang : "Another one bites the dust" 2) "the other" is the second of two things. I have two arms. I hurt my left arm. My friend says: "Did you hurt your right arm?" "No, it was the other one." "I only want one of the gloves, but the sales clerk told me you can't have one without the other." 3) "other" is only an adjective which is usually used with plural countable nouns ("other people"). The pronoun is "others" ("Where are the others? They should be here now.") "Another", "the other" and "others" act as pronouns and adjectives.

"Another" refers to something you want for a SECOND time. For instance, you have already eaten one apple. You want another. "Other" is something you want in place of the first thing. For instance, you prefer the other film in place of this one. These rules don't always follow. For instance, this apple is bad. I don't like it. I want another. The above sentence is correct. Another has other uses such as "Let's do this another day" meaning "I prefer to this a different day". Overall, the rules I said work in the way you are using these two words. However, there are colloquial uses, and it will just take practice using them. Good luck :)