From Rome to Chianciano

Dear Friends , I m doing a surprise to a lovely woman : my grandmother !

She s drinking this so special water in Chianciano terme , and I would like to join her for a week end !

I m arriving at Rome airport , but I don't know how to go from Roma Fiumicino to the CHianciano Terme ? I heard that there was a train but were to catch it ? Do I need to book a ticket ?
Sos Help needded :)