Day trip from Florence to Siena (no additional stops)

Bus. It is direct, takes to the upper town, is faster and more frequent.

There are at least four bus lines that make this journey from Florence to Siena taking 1h 15m. The bus drops you off across the street from Siena’s old town. Do not take the train which is longer and then you need to call a taxi from the station to get to Siena’s old town.

Either the bus or the train will get you where you want to go.
From the train station there's a series of escalators in the shopping center right across the street that will get you up the hill and into the city center without too much bother. Alternatively, you can grab a taxi (about 12 Euros) that will drop you right at the Campo.