Learn Italian: Voi avete il libro di mio suocero? - Do you have my father-in-law's book?

Normally, Italian possessives need a definite article (like in il mio libro). However, there's a big exception: singular family members! Because suocero (father-in-law) is just one family member, it drops the article and we just say mio suocero instead of il mio suocero.

Why does the sentence use di instead of an apostrophe 's' for possession?

Italian doesn't have an apostrophe 's' structure. Instead, you have to flip the order and use di (of). So, instead of "my father-in-law's book", Italian literally says "the book of my father-in-law" (il libro di mio suocero).

Is the word Voi required here, or could I just start with avete?

You can absolutely just start with Avete. Because the verb form avete specifically means "you (plural) have", the pronoun Voi is optional. Including it here just adds a little extra emphasis, like asking "Do you guys have the book?".

How do I know this is a question without a word like "Do" at the start?

Italian doesn't use helper words like "Do" or "Does" to form questions. You simply use the exact same word order as a regular statement (Voi avete means "You have") and make it a question by adding a question mark in writing, or raising your tone of voice at the end when speaking.