You must take a train to Pisa and then transfer to a train to Firenze. On the trenitalia.com site, you are now taken to a parent site. The trenitalia link is on the left and about half way down. Be sure to use the 'English' link in the upper right. Also, use the english spellings, not the italian spellings. The english site does not speak Italian.
Bottom line is you are looking at local trains all the way and I don't think that you can book from outside Italy. There are no reserved seats on local trains - just like a bus - first come, first served. If you want to sit, take first class - it's only a few dollars more.
Radiance of the Seas - Nov 2006
Legend of the Seas - Jun 2007
Costa Fortuna - Mar 2008
Legend of the Seas - Oct 2008
Celebrity Constellation - July 2009
MSC Orchestra - Jan 2009
Navigator of the Seas - March 2009
MSC Poesia - November 2009
Jewel of the Seas - June 2010