Follow the signs to the People Mover, it makes 2 stops and you want the last one.
Get a ticket to Florence either at the counter or at one of the automatic machines. Push the UK flag to make it work in English.
At Pisa Centrale Look for you train number on monitors, not for your destination. When they post the track number, head to it, time-stamp your tickets and get on the train.
As you already know, the blue signs by the platforms will say "Firenze S.M. Novella" not Florence.
Pisa is a through station, odds are that you'll have to use the subway connecting the tracks.
If you can find your flight in an huge airport you can find your train in a 17 tracks station.
You can get a good idea of the level of service on trenitalia.com/tcom-en . Enter Pisa fermata aeroporto in the "from" field, a day of travel before June 11 and an hour of departure around the hour your flight is supposed to land in Pisa.