I have visited the monastery three times (each time staying for a week or more). I love it there. It is a very holy place. The community there is wonderful. To visit them, just get in contact with the guest-master. They have a very nice guesthouse you will stay in and they typically allow for 3-day visits, unless alternative arrangements are made.
For information on visits, its good to start with the visitor's guide:http://www.holycross-hermitage.com/wp-content/uploads/visitors_guide.pdf
I guess the way a visit "works" for a layperson is to share in the grace of the monastic community. This can be done by asking to help out with chores, going to services, seeking spiritual instruction, etc. Is there anything specific you would like to know?