Pisa airport - around 70km from Florence is served by direct flights from the UK, although Florence itself can be reached by flying indirectly through another European city such as Paris or Milan.
Many packaged holidays to Florence already include a transfer from the airport to your hotel, although if you arrive without one, you will find that taxis and buses operate frequent services into the city. A phrase book is handy for speaking to the taxi drivers, and it is important to explain that you do not want to go on a tour of the city on your way to the hotel, because otherwise you can find yourself with a hefty fare once you arrive.