Barbara,
As Roberto mentioned, you can easily do that trip yourself, which will allow more flexibility in the timing rather than being limited by a schedule imposed by the tour company. I've done that trip, and it's very easy.
In order to see as much as possible, it would be a good idea to get an early start, and the 07:08 departure that Roberto mentioned is one of the quickest. I'd suggest starting in Riomaggiore. After a quick walkabout there, take the local train to Manarola for a look there. You could perhaps also travel by boat, but I haven't checked the schedules. While in Manarola you could take a walk on the short section of the Via dell' Amore that's currently open.
Then continue by train to Cornigila (boats don't stop there). As the town is way up the hill, you'll either have to pay a small fee to use the shuttle, or walk up about 300 steps. From Corniglia you can either take the local train to Vernazza or hike the Sentiero Azzurro trail (a Park Pass is required, which you should be able to buy at the small hut at the beginning of the trail or at local rail stations - as I recall, the Pass has to be validated before first use). Be sure to take lots of water!
From Vernazza you can again either take the train or boat or hike the final section of the Sentiero Azzurro to Monterosso. Note that this is the most challenging section and there will be a steep decline at the Monterosso end. I'd allow more time for Monterosso, as it's the largest of the five towns and has both an "old town" and a "new town" so there's more to explore (lots of interesting small shops, especially in the "old town"). Have a fine hot meal at one of the restaurants there and then take the train back to Florence in the early evening. Be sure of the train times though, so that you don't miss the last train of the night!
Note that the trains you'll be using on that route will likely be a combination of Freccia / InterCity / Regionale. Some segments will have compulsory reservations and of course DON'T forget to validate tickets for Regionale trains prior to boarding!