Florence to the Dolomites

Trains do go up into the Dolomites through the Val Gardena and through Cortina. If you won't have a car then I recommend Cortina although this is a very expensive little town. Think Aspen or Telluride - lots of Rome license plates! A day hike from Cortina is a very reasonable endeavor - take the gondola up and pick a trail - great views and tremendous mountains! We have hiked extensively in the Dolomites and it is safe and easy to navigate without a guide. We have never stayed in Cortina - always over in the Val Gardena or up in Brixen. Another place you might consider staying is Castelruth - you can take the train up into the Val Gardena and then a bus to Castelruth. From there you can catch a gondola up and hike in that part of the Dolomites. We have actually never made hotel reservations in the Dolomites - we go to the tourist office, see what's available, they make the call, book it for us, and then give us directions on how to get there! We've stayed in cute chalet-style hotels, guesthouses, and campgrounds all over the area and have never had a bad experience - people in this part of the world are very hospitable, kind, and wonderful hosts.
Go to the trenitalia website for fares.

Dolomites are a large area. Trains do NOT go through the Val Gardena or Cortina. For the Val Gardena take a train from Florence to Bolzano, then proceed by bus. Wherever you choose to go, the best way is probably a train to Bolzano, the provincial capital of Alto Adige (Sud Tyrol) then a bus from there. For train schedules look here www.trenitalia.com From Firenze SM Novella to Bolzano. Then search buses to whichever destination. The train trip from Florence is about 4 hours (plus/minus20 min) and the cost is about 40 euro one way. There are no night train options. Buses cost and duration varies depending on destination, but it's not that expensive. Google the following words:
Autobus da Bolzano a (enter destination town).