Catching calcio fever
To Italians, calcio (soccer) is something akin to a second religion. You don't know what a "fan" is until you've attended a soccer match in a country like Italy, and an afternoon at the football stadium can offer you as much insight (if not more) into Italian culture as a day in the Uffizi.
Catch the local team, the Serie A ACF Fiorentina—referred to as La Viola for the purple of their uniforms—September through May.
Most games are Sundays at 3pm, with a few other games at odd days, like Satuday afternoon or Wednesday night.
The cheapest tickets are in the curve, the "curves" at either end of the pitch. The home team Fiorentina fans sit in the Curva Fiesole, so if you want to be in the beating, screaming, fan-crazy heart of the rowdy action, sit here. The views of the actual match aren't the best, but if you want to pick up the local soccer chants (at just some novel Italian curses), it's the best spot.
You can buy tickets ahead of time (starting at €14 ($17))—online or at the downtown 'Fiorentina Store" ticket office on Piazza Mercato Centrale—at the official ticket office (from €20 ($24)) two blocks west of the staidum at Via delle Sette Santi 28r (at the corner with Viale Giovanni Dupré, or at the stadum itself three hours before a match.
Bonus: Your ticket gets you free transport on the bus system on game day.
Also, bring a photo ID (passport is best) both to purchase your tickets and to the stadium. It a crackdown-on-hooliganism thing. (And for god's sake, keep the passport in your moneybelt at all times except when you need to show it to security.)
Arrive at least 30 minutes early; stay for the 1.5–2 hours of the game.
All told, bank on spending at least 3-4 hours.