Mindy, having flown out of Florence a few times, I would suggest getting there at least two and a half hours before your flight.
I flew out of there three weeks ago...my flight was due to leave at 08:30 for Amsterdam.
There was one check in agent for three flights KLM/Air France/Delta, and a huge lineup of annoyed people.
This had been the case on other flights from there in the past.
Eventually another couple of agents sauntered in, chatted with their colleagues, and eventually opened their desks.
I did make my flight, so did my checked bag, but no time for a last coffee before boarding!
If you have carryon only, you can, I believe, use a machine in the area to check in.
And, as always, check in online 24 hours before.
It's never been the most efficient airport in my experience!
If you're going by tram to the airport...now that IS efficient!
Buy your ticket ahead of time in a Tabaccheria shop...same price as local bus tickets.
People were having trouble with the ticket machines at the tram stops, both to and from the airport.
Have a wonderful time in Italy...where are you going this time?