I recently did a tour for a great group of Aussie high school teenagers. 
When speaking with their lovely (and cool) English teacher who was accompanying them through Europe, she told me an amusing story. When they were in Rome, she would start each day with a coffee in a local bar. She told the students that they should come with her as it would be a perfect time to write in their journals, something that they had to do in any case at some point each day as part of an assessment. She told them that it was a good place to experience Italian life. Initially, the teenage boys weren’t overly keen and the first few times they went reluctantly –  coffee was something older people drank and was maybe even a bit of a sissy drink, so the whole thing was a bit naff, the opposite to a pub and beer. That was until three uber cool young Roman guys rocked in one morning to the café where they were, helmets in hand for their vespas, that they had casually, and probably illegally, parked outside, sporting cool sunnies and decked out in the ubiquitous Diesel jeans and some cool and, no doubt, snugly fitting tops. They ordered three macchiato coffees, laughed and joked with the barman and with each other, drank them, paid, and then sauntered out, all in the space of about five minutes. The English prof noticed that the three male Aussie students were mesmerized, and, early the next day, they asked when they were next going to the coffee bar. On arriving at the bar, all three ordered a macchiato!   
Un caffè –  an espresso, a shot of coffee in a small cup.
Un macchiato means ‘stained’ (it is the past participle of the verb ‘to stain’, which is macchiare) –  served in an espresso cup, the shot of coffee is stained with a dash of milk. 
Un cappuccino –  so named for the colour of the milk coffee which resembled the 
habit of the cappuccin friars ( a branch of the Franciscan order who wear a lighter brown greyish habit).
Un caffè americano –  is a shot of espresso served in a cappuccino cup with hot water added. If ordered when seated it will often be served with a little jug of milk. If ordered at the bar standing there should always be a little jug of milk. If there isn’t, then ask.
Un marocchino means Moroccan –  a shot of espresso in a small glass cup 
filled to the top with milk and cocoa added on the top as well as in between the 
milk and coffee. (this is not diffused in all areas of Italy). 
Un caffè corretto means a corrected coffee – an espresso with a shot of grappa. This could be good for suffers of Stendhal syndrome in Italy, a replacement for smelling salts to regain composure!
There are two different price systems in the coffee bars, the price differing according to whether you sit or stand at the bar (what Italians do). If you stand at the bar, then you pay before at the cash register and take the receipt to the bar, give it to the barista and tell him what you want. He will rip your receipt and serve you your coffee, which you consume standing at the bar. If you sit at the table, somebody will come and take your order and bring you a bill. The price goes up according to  the service charge. Beware – it can sometimes triple, especially for seating outside in the piazzas. Prices are listed in the menus on the tables.  
Italians drink cappuccino at breakfast time, until mid morning. Then they switch to a macchiato or an espresso for the rest of the day. They find the Anglo-Saxon habit of a cappucino after dinner truly puzzling.  It is all about mixing too much milk with digestion, which could cause havoc!  Instead, they have an espresso, or even better, a digestivo (something like Montenegro) – or better still, both! 
Favourite coffee places in Florence:
Cafe Giacosa Roberto Cavalli

Cantinetta dei Verrazzano in via dei Tavolini – I must admit that I have coffee here every day. It is very good, they are very nice and the cakes, pastries and 
focaccias are also very good. The benches and table tops are of Carrara white 
marble which adds to the   atmosphere of eternally good things…
Café Giacosa – Roberto Cavalli, next to the Cavalli store on via Tornabuoni – here the good coffee is always served with the addition of liquid chocolate, so 
Café Giacosa inside Palazzo Strozzi on via Tornabuoni –  run by theCaffé Giacosa mentioned above and is a lovely place for good coffee, cake or light lunch. Never too crowded and seating in the internal courtyard. 
Chiaroscuro in via del Corso – serves good coffee with yummy variants that are written up on a board above. A friend of mine always orders a marocchino here…….

Cafe Giacosa Palazzo Strozzi