Yes, it's 90 minutes by high-speed train from Roma Termini to Firenze Santa Maria Novella (Florence's main train staton). There are many trains making this run every day.
MaryPat, your link doesn't work.
Go to this site:
Choose "Roma Termini" in the "From" dropdown box, and "Firenze S.M. Novella" in the "To" dropdown.
Enter your preferred date and time of travel to Florence, and the same for "Return"
Enter number of passengers and hit "Search"
Your options for going TO Florence will come up. Toggle between the departure and arrival stations at top of page to see your options going back to Rome. Explore the prices available by clicking the little black arrow to the right of the price shown for the time of train you want.
Italo high-speed trains also make the Rome>Florence run; you can probably figure out their site without much help. :O)
In both cases, your tickets would be for specific trains, at specific times, for specific carriages (by class of ticket you bought) and for designed seats. You do not have to validate tickets for these types of trains before boarding. Understand that the lowest-priced tickets are very likely to sell out in advance; the price will be more - sometimes a lot more - if you wait to buy them on the day of the journey, and all that's left are the more expensive tickets.
I'll agree that there's so much great stuff to see in Florence that it's a shame try and do it on the fly just to say you did! Most of the better attractions are also indoors, and may require advance, timed-entry tickets.