Latin is as Bellarmine said the official language of the Holy See and the Vatican City State, but the working language of the Vatican is Italian. Given its location in Rome, the Vatican’s use of Italian makes perfect sense. As for Latin though, fewer and fewer seminarians and priests today are familiar with it as in the past, and lay people seldom study it; but official church documents are still published in Latin.Although knowledge of Latin is not emphised as it once was (pre-Vatican council of the 60s) it is still part of the studies of any candidate for the priesthood. And of course, any serious scholar who wishes to understand the great thinkers of the church, such as Augustine or Aquinas, needs a good working knowledge of the language. As the Papal Latinist, Reginald Foster, O.C.D., puts it: “You cannot understand Saint Augustine in English. He thought in Latin. It is like listening to Mozart through a jukebox.”
To answer the original question about “what language monks use” in day to day activities, the answer is the vernacular, the language of their country. I believe the questioner meant currently (that saves a lot of chit chat about the past) and in the United States.
Since all monks are not priests knowledge of Latin is not now nor ever was a requirement for entering the monastic life. In the commonness of monastic thought there is great diversity and you will find that some emphasize communal prayer and express it through Latin chants. However daily business is conducted in English. As an aside, I have a friend who said he could count on one hand the monasteries in the U.S. that were ethnic and spoke in the tongue of an eastern rite. But that is another category altogether. He also told me he knew of a monastery in the U.S. that spoke only Russian. They were preparing themselves to move their community to Holy Mother Russia when the cold war ended. I am not to sure about that. When my friend said, as he often did, that he could ‘count on one hand’ he meant it quite literally as one is all he had. So I was never sure if what he said added up.
I am curious as to why you asked the question. Were you thinking of signing up? Was the though of having to study Latin putting you off? Or are you looking for a place to immerse yourself in the language? Or maybe it’s because you are, as the rest of us here on Historum are, just plain curious.