Well, I assume you know what "other" means. So, you will always use "another" if the subject is singular (only one) and as long as there is no definite article (the). I need another book. The book is only one and there is no definite article "the" or words like "any", "some". But: I need the other book. The book is only one, but there is "the" so "an" cannot be introduced. I need other books. In this case the noun (book) is plural, so "an" cannot be used. I need any book. As for "someone" and "somebody", they used to be different but the difference is today considered to be obsolete, so you can use them interchangeably.

You can find a real clear explanation here: https://eslteacher.org/another-vs-other-vs-the-other/

other music, other people (countable, uncountable). (plural) Another person, another friend (only singular and countable) someone somebody= the same. the only difference is that someone sounds a little more polite.