Purchase a ticket and join the crowds at a game at Stadio Carlo Castellani. If there's nothing on while you're in town, you might like to check if there's a tour of the grounds.
This Empoli sporting facility is a good spot to start your day of sightseeing. There's loads to see and do nearby, like Casa Natale di Leonardo, San Miniato Cathedral, and Leonardo Museum. Wander around at your leisure at Stadio Carlo Castellani before heading to these other fine sights.