Bus and train travel from FCO to Porto Santo Stefano to Siena back to FCO hotel

There is no train service. You need to get to the bus station in Rome but at this moment I don't where it is. I am checking.

My understanding is there is train service from FCO to Orbetello, which is very near Santo Stefano. My apology for misspelling Orbetello in my original message. Then bus to Santo Stefano?

The train from Fiumicino Aeroporto (FCO) station to the Orbetello-Monte Argentario station requires actually two trains.
The first train goes from the airport to the city of Rome.
Once in Rome you change trains to go up to the coast to Orbetello.
The specific station where you make that train change in the city of Rome varies depending on which train and time you take it.
Some require the change at Roma Trastevere station, some at Roma Ostiense, some at Roma Termini (which is Rome's main station)

Go to the website below and enter
FROM: Fiumicino Aeroporto
TO: Orbetello-Monte Argentario
DATE: enter the date of your travel
TIME OF TRAVEL: Approximate time of travel, or put very early in the morning to see all trains.
The website will give you many solutions. Depending on the solution selected you will have to change trains in Rome at the specific station indicated (see the details info to see which one).
https://www.trenitalia.com/en.html

Once you alight the train at Orbetello you can take a bus to Porto S. Stefano.
The bus schedule is below.
https://www.giglioinfo.it/isola-del-giglio-info/orario-autobus-orbetello-scalo-porto-santo-stefano.pdf
and also here
https://www.at-bus.it/en/timetables.html#modTimetables_collapseExtraUrbanLine
Select Suburban services, then Servizi Extraurbani GR, then select bus Oo1 to dowload the timetable in PDF

From Orbetello to Siena first you need to reach Grosseto, the Provincial capital.

You can go to Grosseto from Orbetello via train, from the same station I described in the previous comment. To go to the station you take the same bus.

You can also take a bus from Porto Santo Stefano directly to Grosseto, but there aren't too many buses, so it depends on your schedule. Trains are more frequent, but if you can take the bus below, it's less hassle.
https://www.at-bus.it/en/timetables.html#modTimetables_collapseExtraUrbanLine
Select Suburban Services, the Servizi ExtraUrbani GR, then select bus 39O to download timetable in PDF.

Once in Grosseto you take the bus 51G to Siena
https://www.at-bus.it/en/timetables.html#modTimetables_collapseExtraUrbanLine
Select Suburban Services, Servizi Regionali su Gomma, then select bus 51G to download timetable in PDF

You can buy tickets at authorized retailers (basically Tobacconist shops displaying the Autolinee Toscane logo), ticket machines (where available), or via TabNet app. Details are below (click on tickets then select the Extraurban tickets section)
https://www.at-bus.it/en/