From the North, the main line between Florence and Rome has a station at Terontola (on the branch line to Lake Trasimene, Perugia, Assisi, Spello, and Foligno), so coming from Florence  take one of the dozen daily trains to Terontola/Cortona (1'/2 hr.) that meet up with a connecting train to Perugia (35 to 50 min.).

From the South, the main line between Rome and Ancona has a station at Foligno (on the branch line to Spello, Assisi, Perugia and Lake Trasimene), so coming from Rome, take one of the nine daily trains on the line to Ancona, stop at Foligno (1 hr., 40 min. to 2 hr.), where you can transfer to a Perugia-bound train (30 to 35 min.).