To Ashley:
You have the choice of two companies (the first State owned, the second private, both are similar in quality and price):
1. http://www.trenitalia.com/tcom-en
2. http://www.italotreno.it/en
The trip is 90 min long (each way)
Florence central station is called: FIRENZE SANTA MARIA NOVELLA (often abbreviated in FI SMN)
Rome central station is called: ROMA TERMINI
You need to enter the Italian spelling of the above stations in the website.
You don't need to purchase ahead of time online. You can just wait and purchase on the spot. Pre-purchasing online ahead of time gives you a chance of buying discounted tickets (called Economy and SuperEconomy), however be aware those are restricted. They are non refundable nor changeable therefore you need to be reasonably certain of your travel plans otherwise if you miss the train you book you are out of your money.
To all others.
Let's try to stick to the topic and answer the question instead of trying to tell people where to go and for how long and what they should do with their life. People may have their reasons why they only have time for a day trip to Rome. Some people may actually prefer to spend more days in Florence or Venice or maybe Poggibonsi than in Rome just because. Maybe they only have 3 nights in total in Florence and would like to have a quick glimpse of Rome without having to switch hotels, which is time consuming. Why are we trying to impose our preferences on others? Especially when the question was very specific and didn't ask for an opinion on how many days to allocate to each place.