Each school can and do things little different.
Based on best experience, we didn't fly, we drove. Coach asked prospect if he wanted to stay the night at the dorm where the baseball boys were and it was optional.
Overall experience was about 5 hours. Arrived early, met coaches, toured campus, including weight room, dorm room, practice facilities and field. We then made way to admissions office to go over requirements and received info package. Lunch was next and paid for by school. After that, back at office where it is explained to you why you were recruited and where you fit in their program followed by a question and answer period. Then an offer is made, an NLI, and then a timeline is set to accept it, in this case 14 days to talk it over with family. Yes, you are able to stay and practice with the team on the field until the whole team arrives then its official practice and you have to leave the field and watch. You can also use batting cages so coaches can evaluate you. If the following day they have a home game, you can attend along with 2 others at their expense. If not you are free to go home.
Then you keep in contact with the coach, going over any missed details or questions. You can ask for an increase in athletic aid if you think you can get more, then settle on accepting the offer. Then you apply to the college and get things going from there.