I am having trouble getting a train to come up for a Saturday travel. Do the trains run every day in Italy? I am trying to figure out how to get from Venice to Perugia.
Yes they run every day.
Since you will be traveling, in part, on Regional trains (basically commuter trains) the timetable for Regional trains is available on line only for the 7 days ahead. Therefore in order to get the schedule you must use a date in the next 7 days. Use next Saturday as a test, the timetables don't change much from year to year, therefore the train will be available when you travel with only minor, if any, time changes.