Coming from Pisa Airport Aeroporto di Pisa Galileo Galilei, take the bus to railway station Pisa Centrale travel time approx. 0h10, single ticket €1.30. From Pisa Centrale you can take a direct train to Grosseto, travel time approx. 1h20, single ticket €17.50 Intercity or €21.50 Frecciabianca.
From Rome Fiumicino Airport Aeroporto di Roma Fiumicino Leonardo da Vinci, the cheapest option is to take the regional train to Roma Ostiense, and from there the regional train to Grosseto travel time approx. 2h45, single ticket €19.75. Alternatively, take the Leonardo Express to Roma Termini, and from there the Intercity travel time approx. 2h30, single ticket €31.00 or Frecciabianca travel time approx. 2h20, single ticket €41.50.
Frome Florence Airport Aeroporto di Firenze Amerigo Vespucci, take the bus FSBusItalia to the main train station Firenze Santa Maria Novella, travel time approx. 0h15, single ticket €1.30. From there, you can take various regional trains, most of which pass through Pisa Centrale, where you can also change to an Intercity or Frecciabianca. Travel time approx. 3h, single tickets from €17.50.
See the website of Trenitalia for schedules. From Grosseto railway station, it is a 10-15 minute walk to town centre.