Bus: The bus system is quite good, reliable for normal service. The #7 bus goes from San Marco (downtown Florence, near the Duomo) to Fiesole. The EUI is in San Domenico, on the way to Fiesole. The EUI stop is announced, but keep your eyes open. You can buy a ticket on board for 2 euros, but they are often unavailable. Your best bet is to buy a 4 or 10 ticket pass. Bus tickets can be bought in the newspaper shops or some coffee bars (those with the T (tabacchi) sign outside).
You can also look at these links for more info: