The best way to do a day trip to Rome from Florence is by train.
We decided to start our day at the Colosseum and Roman Forum, then move on to the Vatican Museums/Sistine Chapel in the afternoon.
Rome has a handy and easy-to-use Metro system. I highly recommend it if you want to get around the city quickly and cheaply.
The Colosseum is a great choice if you only have a short time in Rome since you essentially get two major sites for the price of one.
The Forum was once the center of Roman life, but to the casual 21st-century visitor it will look like a jumble of ancient ruins.