Trenitalia Frecce operates a train from Grosseto to Cinque Terre every 3 hours. Tickets cost $30 - $45 and the journey takes 2 h 5 min. Trenitalia also services this route hourly. Alternatively, FlixBus operates a bus from Grosseto to Cinque Terre once daily. Tickets cost $10 - $18 and the journey takes 2 h 20 min. 3 other operators also service this route.
From Grosseto train to La Spezia Centrale then train to Corniglia. 2 h 43 min 33€. From Grosseto bus to Pisa, bus to La Spezia - Instituto Cardarelli, bus to La Spezia Centrale, then train to Corniglia. 5 h 40 min 23€. From Grosseto drive to Cinque Terre. 2 h 54 min 38€.