Deb, you absolutely do not need any reservations for these trains - even if there was one which DID have reserved seating. Just buy your tickets on the day of your journey. We only pre-buy tickets if it's a very fast, direct, city-to-city (say, Rome to Florence) train that we might be able to land cheaper tickets for as those tend to be more expensive.
I can't tell you exactly how long each of these runs will take as it depends on which train you decide on. For Firenze S. M. Novella to Vernazza, for example, trains can take anywhere from about 2.5 hours with two train changes, to 3.5 hours with one train change and a longer wait time between them. It may also depend on which of the 5 villages in the CT you're trying to get to. Same with going from the CT to Pisa.
What you need to do is get onto the Trenitalia website and punch in your dates, departure/arrival stations and desired time of departures.
http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=4ddd1a035296f310VgnVCM1000005817f90aRCRD
Do use the Italian names of the stations: Firenze S.M (Santa Maria) Novella is the main station in Florence, and you can just use any of the names of the 5 villages for the C.T. For flying out of Pisa, you'll want to go to the main train station - Pisa Centrale - and then hop a shuttle bus to the airport as the trains currently don't run there. See this:
http://www.pisa-airport.com/aeroporto_di_pisa_76.html
This may be helpful as well: just reverse the directions as you're going TO the airport:
http://www.turismo.intoscana.it/allthingstuscany/aroundtuscany/from-pisa-airport-to-the-train-station/
Make sense?