The easiest way to reach Tivoli from Rome is by COTRAL bus from Ponte Mammolo metro station (Line B). Buses run every 15 to 30 minutes; the express via the autostrada takes about 50 minutes, the slower local service via the Via Tiburtina around 75 minutes. Buy tickets at the metro station before boarding.
The regional train from Roma Termini or Tiburtina is an alternative — about an hour, but the station is on the lower edge of town, a steep walk or short bus ride up to the old centre.
By car, take the A24 autostrada from Rome (exit Tivoli) — about 30 minutes outside rush hour. Parking inside the old town is impossible; use the large lots near Villa d'Este or by the train station.