Translation:The book is next to the newspaper.
Excellent question! The short answer is this: you do not put articles before pronouns! :) Μου is a personal pronoun.
The long answer now:
In order to make some sense of this, firstly you need to know that στην=σε+την (=to+the), so what we now use as an article is in fact a preposition+the definite article. Secondly, you need to know that personal pronouns have two forms, one is strong and one is weak. It is possible to use a structure that includes σε+pronoun, but pronouns do not need to be preceded by articles of course. So, you can either say "(Εσύ) Είσαι δίπλα σε εμένα" (σε+strong pronoun form) meaning "You are next to me" word-for-word or "Είσαι δίπλα μου", which means exactly the same thing but uses the weak form of the pronoun and consequently drops σε.
According to similar examples, the answer should be ,"next to". "By" is here not a good translation, anyway.
I know I replied to another similar comment of yours in another discussion, but I'll reply here as well for other users that may have the same question:
“Near = κοντά, next to = δίπλα.”
I usually mistake those prepositions en Greek. I see κοντά and I think it means "next to"; the same with δίπλα. Does anyone know a mnemonic or etimological rule to help me use the right one for "near" and "next to"?