what is the best way to travel from Florence to Sorrento?
If you want a private driver & tour (there were 8 adults in our party so it proved economical) Try "Your Tour in Italy" at: http://www.yourtourinitaly.com/joomla/ They picked us up at our hotel in Rome, took us to Pompei (for a 2 hour tour) then dropped us off in Sorrento. After an overnight there we called them back and they picked us up and took us back to our Hotel in Rome. They're fabulous.
By "best," do you mean cheapest, fastest, fewest transfers, or something else? How many are going, and are there special circumstances (like poor mobility or lots of luggage)? Jan's suggestion of a car and driver service is certainly easy, and as she pointed out, for a large group may not be outrageously expensive per person. But for one person, it would be extremely expensive. She was going from Rome; from Florence, it's much more money. You can take a train from Florence to Naples, then the Circumvesuviana train or a boat from Naples to Sorrento. With the Florence to Naples portion booked in advance, this would be cheap (the Circumvesuviana is like a bus on rails, and can't be prebooked but is very cheap). There may be buses as well, but I don't have details of these. I'm not aware of a "one seat ride" between the two, except in a car (either a taxi service, or one you're driving yourself).
"Best" is in the eye of the beholder - for me, it would be by private helicopter with an in-flight personal masseuse and gourmet chef, and someone else paying for it all. If you don't have the luxury of having someone else to pay for such extravagances, I can't think of a single good reason not to just take the train: Florence > Rome > Naples (change to the Circumvesuviano in Naples) > Sorrento. Simple, easy, safe, comfortable, not expensive, enjoyable.