Spoleto has a railway station on the Rome–Ancona line, with direct trains from Rome Termini taking about 90 minutes and from Perugia about 45 minutes. The station is a 15-minute walk from the old town, or take a local bus up the hill. From Florence, you usually change at Terontola or Foligno.
By car from Rome, the A1 motorway to Orte then the SS3 (Via Flaminia) north is the most direct route — about two hours in light traffic. Parking inside the old town is limited; the car park at Piazzale Ponzianina near the funicular is the easiest option.