Travel To Amalfi from Florence

You can do it on the same day. Florence to Naples is about 3 hours. Naples to Sorrento another hour by Circumvesuviana commuter train. Then from Sorrento to Praiano it's another hour on a bus (gorgeous bus ride. Stay on the right side of the bus)

Firenze to Napoli
http://www.trenitalia.com/

Napoli to Sorrento
http://www.eavsrl.it/web/it

Sorrento to Praiano
http://www.sitasudtrasporti.it/archivio/Download/corse/sitasud/Campania/Salerno/8e9cb954-7c9c-48f1-86e5-c5e8444f036e_QUADROXIV_2015_AUTUNNO_2.pdf/0

It's a long way from Florence to the Amalfi Coast. Just from Rome to Naples is 150 miles.
Have you considered just visiting the Cinque Terre instead? You just take the train over to Pisa and a short distance north to La Spezia. Then a few minutes on a local train and you're there.
The C/T is a very popular area and would be a great substitute for Amalfi.

You can also take the train from Florence to Salerno and then the bus. Wont be any quicker as it will take about 4hrs from Florence to Salerno (with a change) but it means you are on the much more comfortable trenitalia trains for the whole train leg and avoid the circumvesuviana commuter train.

Not true about the change of trains between Florence and Salerno. There are three daily departures from Florence SMN station between 8AM and 12 noon--the Fresciarossa 9503, 35563 and 9521--that do not require a change of trains. Only stops are at Roma Tiburtina, Roma Termini & Napoli Centrale, before arriving at Salerno Centrale. Durations are between 3:20 and 3:40.

From the Salerno bus station (right next to the train station), you would take the bus 1 hour to Amalfi, change buses, then the 2nd stop about 25 minutes later on the next bus is Praiano.

So...pick your poison, as it were. From what I can decipher, to get to Praiano your way, after 2 hrs 45 min Florence to Naples, the Circumvesuviana from Naples would be a little over an hour to Sorrento, then another hour and a few minutes by bus to Praiano.

Depending on how quickly you can catch the next bus or train, both routes look like they'd take about the same time, as mph states above. And because of the geography & logistics, there's a certain amount of backtracking no matter what. Either 2 trains and 1 bus...or 1 train and 2 buses! You definitely can do it all on the same day--just start early. Enjoy!

I've taken the Eurostar from Florence to Naples, and then the train to Sorrento in one day with plenty of time left over to explore (or travel further by bus). I took the 8:00 or 9:00 AM train out of Florence. It was easy and pleasant, I thought. Another day I took the bus to the Almalfi Coast (Positano), which was a beautiful ride, but we were staying in Sorrento so we made it a day trip. You could make the entire journey in one day. However, you should make sure you get a bus along the coast during the daylight hours so you can enjoy the beautiful views. If you need to stay overnight along the way, I'd suggest you overnight in Sorrento as that will get you close enough not to waste too much of the next day. However, I suggest you go for it and keep the travel to one day. I can't tell you the length of time specifically as it was a while ago, but we had plenty of the afternoon left to explore before dinner, and would have had time to get to Positano before dinner.

You can do it either in one day, or in two days with a stop in Napoli or in Sorrento. I have done it in all three configurations. The Amalfi Coast is spectacular, my favorite place is Praiano.