"Let's speak quietly in the library."
Translation:도서관에서 조용히 말해요.
Usually if you want to use that version of the verb (I'm blanking on the name), you would say 말한다.
Secondly, since it's saying "Let's" you'd have to include that somehow. In low formality, you change nothing, hence "말해요" but informally you'd say 말하자. Formally you'd say 말합시다.