what is the travel time by train from genoa,italy to florence, italy?

According to RailEurope, it's 2 hours 5 minutes

It depends by the train you choose... a Eurostar, which is faster, takes 3.30 hours, when a slower regional train can take 4.30 up to 5.30 hours (i.e. the one travelling during the night).
Anyway you should change your train either in Pisa or in La Spezia, nearly after 2 hours from the departure.
You can browse the timechart at
http://www.trenitalia.com/en/index.html