If you have only one day, here is a suggested itinerary starting from the train station:

1.  Go to San Lorenzo (nice church to see).

2.  Then the Accademia (where David is, worthwhile, make sure to check this!)  You must prebook to avoid waiting in huge lines.

3.  Go to Baptistry and Duomo at Piazza del Duomo (very impressive cathedral with beautiful dome), Take time to climb the dome - the view of Florence is breathtaking! 

4.  Walk then to Piazza della Repubblica (nice area to have a drink).

5.  Walk over to the Palazzo Vecchio (make sure you go into the Palazzo, the first of Medici Palace,  it is splendid). It is located at Piazza della Signoria, which is filled with wonderful sculpture. This another lovely Piazza to have a drink or gelato while enjoying the sunshine.

6.  Cross Ponte Vecchio (oldest bridge in town, check out the jewelry shops on the bridge).

7.  Head down on down the Via de Guicciardini to Palazzo Pitti ( the second Medici palace) and take a stroll in the Boboli Gardens.

8.  If you have time, walk up to Piazzale Michelangelo for incredible views over the city

One should really try to spend more than one day in Florence...to experience the wealth of art, sculpture, architecture and food. Three nights is an ideal amount of time for a first time visitor.

This is a lot to do in one day and it may not be possible to fit it all into one day, so do read a decent guide book and tailor your itinerary to suit your interests. You will notice that the Uffizi Gallery has not been listed and many people feel this is a must-see. If you have a particular interest in Renaissance and religious art then you should go, but be prepared for it to take a good three or four hours out of your day (with advanced reservations to skip the line). You can of course just focus on a few of the most famous paintings and take less time, but you will have to drop some of the above to fit it in.

Other sights that you might like to consider chopping and changing into the above itinerary are the Basilica of Santa Croce (where so many famous Florentines are buried), the Bargello (a must if you have a love of sculpture), the monks cells at Museo di San Marco (for the wonderful frescoes by Fra Angelico), the Palatine Gallery at the Palazzo Pitti (again for lovers of Renaissance art).

Do carefully check opening days and times of each place you intend to visit as they can be very variable.