At the moment the complex is private, inside is an agriturismo and a conference hall. I can't say there's much to do here for a tourist, but you can stop by, to take a picture from outside.
We would hardly know about this place without the fact that it is the main filming location of The English Patient (1996), one of the most famous films in history, winning nine Academy Awards.
If you don't live in the monastery, you can still walk outside and see the cypress alley and the cemetery where Juliette Binoche's character met Willem Defoe's character. His role, by the way, was offered to Bruce Willis, but the agent turned it down without notifying the actor, which Willis regretted a lot afterwards.
Getting there: parking 43.128242, 11.651425.