"Another" is used when you already have one of something and want one more (one more ~ another) "other" is used for when you have one of something but want a different one "the other" is used for when you have one of something but want a specific different one Hope this helps! :}

Another - additional ( I want another piece of cake ) Other - selection ( Other English accents are different to understand ) The other - subject ( The other day, I saw my friend )