Ciao!!
Florence to Capalbio will be a long trip but not impossible on public transportation - the thing is I don't think you can do it in one day. Actually, even if you were doing it by car I wouldn't recommend it as a day trip either. Even the car ride is about 3 hours. So you see where I am heading with this... if you really want to get to that area to visit the Tarot Garden, you should plan to spend at least 2-3 days there, the area is beautiful and there is lots more to see that will keep you busy. And a car would make it much easier to move around.
In any case, the trip is still doable on public transportation -- the easiest solution would be take the train from Florence to Capalbio - go to
Trenitalia to plug in your dates to see specific timetables.
The train ride takes about 3.5 hours (actually not bad considering it includes train changes) and there isn't much difference in time it takes to get there whether you pass through Pisa or through Siena getting down to this area of the Maremma. For a random search, I see a train leaving Florence at 6:28am which gets into Capalbio at 10:02am (passes through Siena), the next one is at 10:28am and gets you there at 2:02pm (passes through Pisa).
Once you get into the Capalbio train station, the tarot garden is not too far away. You can take bus # 40/O (10 min bus ride) which drops you off quite close to the garden entrance.
Another alternative: take the bus from Florence to Siena which is a little faster than the train and from there continue on by train.
So you can see how it might be hard to get everything done on one day. From Capalbio you can take the train on to Siena and on to Florence.
If this is your first time to Italy, my impression is that you have misjudged distances. Florence and Maremma is never a day trip - even if the distance is little more than 200km, most of the way is done on a two lane road. And there are so many things and places to see in each place you stop at that, that you should consider 2-3 days in each place and doing day trips in the immediate area, then moving on to another area and exploring that one. It would make more sense to spend a few days in Florence and see Florence and maybe do a day trip into Mugello or Chianti, then move on to Siena and see that area, then move on to Maremma and see that area.
Hope this information is useful! Please feel free to post more questions, I know how confusing it can be to plan the first trip ever but hopefully we can help you get a better idea of what there is to see and do and that your trip will be wonderful.
Also let us know when or what period you're planning the trip for, there are definitely some areas that are better in certain seasons!
