"How do you get from Livorno to Florence? " The train is not difficult. Take a cab from the port to the Livorno train station. about one mile. The Florence station is close to the center of Florence. All the major sights of Florence are walkable from the station. However, be aware that lines at the Uffizi museum and the Academy (for David) are long. I do understand there are ways to make reservations for specific times at a small price.
When we went to these many years ago there was no line delay, but there is now.