Intercity trains, which are faster and stop at fewer stations, must be booked in advance and require a reservation. This can either be done online at the Tren Italia website or by going to the station 24 hours before your departure time.
Local trains are more useful if you are travelling to smaller towns as they stop at most stations. Obviously this means journey times are slower, but tickets will be cheaper than on the Intercity journeys. Tickets can be bought on the day of the journey for local trains.
SITA is the company that runs buses and coaches throughout Italy between the major towns and cities. You can book journeys on their website or go to the bus station in the town where you're staying to buy tickets. Local bus companies run services between smaller towns, in the suburbs and around the cities and towns themselves.
As well as using buses to travel around the major towns such as Florence and Pisa, you can also rent bicycles. Florence has pedestrianized areas throughout the old town where bicycles are permitted and it is very safe to ride. Cities and towns will also have taxis which can be hired on the street, at most railway and bus stations, or you can ask your hotel to book one for you.