The annual German themed Christmas market is up in Piazza Santa Croce - it usually runs until about a week before Christmas. There will also be a market in Piazza Repubblica this coming weekend, Saturday and Sunday the 8th and 9th. And then there are the various weekend markets coming up in several palazzi around the city. Maybe the largest and most well know is the Mercato Nataleperfile (also this coming weekend) at Palazzo Corsini (the Nataleperfile Panetonne are one of the most famous in Florence). There you will find all sorts of hand made goods and gifts, gourmet foods, and more, all inside the very magical setting of the palazzo (they also have lunch which is usally pretty fantastic!).
There is also the AILO Christmas Bazaar which is a fundraiser, and many others. Leave a comment if you know of more.