Sententiously is how someone speaks when they are being sententious: they tell people how they should behave, in a voice that sounds sure and a little superior. The word is an adverb, so it sits on the verb — he spoke sententiously; she nodded sententiously. The feeling in the room is usually: we did not ask for a sermon. It is a bookish, disapproving word, the same as the adjective. You would not use it for a teacher who is simply being clear; you use it when the talking has turned into moral display. Though actually, a person can say something true and still say it sententiously — the problem is the manner, not always the fact.