Learn Spanish (Spain): ¿Quieres el libro?

The verb is querer (to want). It is a stem-changing verb, which means the e in the root of the word changes to ie when we conjugate it for certain people, like the tú (you) form used here.

Does the e to ie change happen in all forms of querer?

No, it happens in most forms, but skips the nosotros (we) and vosotros (you all) forms. So it is quieres (you want) with the change, but queremos (we want) keeping the original e.

How do we know this means 'Do you want' when there is no word for 'Do'?

Spanish does not use helper words like 'do' or 'does' to make questions. The upside-down question mark at the start tells you right away that Quieres el libro is a question rather than a statement.

Why isn't the word tú (you) in this sentence?

The ending of the verb quieres already tells us exactly who is doing the wanting. Because the -es ending is specifically for tú, the pronoun itself is optional and normally left out to sound more natural.