Italian bars in the center of major cities charge more (typically double) if you drink and eat seated at a table rather than standing at the bar or taking your order to go. The further away you are from the main streets the less this rule is applied. When calling into a bar for a coffee or other drink you first go to the cash register and pay for what you want. You then give the receipt to the barman, together with a token tip (5 or 10 cents for a coffee or two).
Restaurants always used to charge a small coperto (cover charge). Some years ago attempts were made to outlaw the practice, with limited success. The rule now seems to be that if you have bread a coperto can be charged but if you specifically say that you don't want bread then no coperto can be levied.
Some restaurants now levy a service charge, but this is far from common. In others a large tip is not expected. The customary 15% of the United States may cause an Italian waiter to drop dead with a heart attack. Round up to the nearest Euro 5 where the check is less than Euros 100 or limit the tip to 5% and everyone will be happy.
The traditional meal can include (in order) antipasto (starter of cold seafood, gratinated vegetables or ham and salami), primo (first dish - pasta or rice dishes), secondo (second dish - meat or fish dishes), served together with contorno (mostly vegetables), cheeses/fruit, dessert, coffee, and spirits. Upmarket restaurants usually refuse to make changes to proposed dishes (exceptions warmly granted for babies or people on special diets). Mid-range restaurants are usually more accommodating. For example, a simple pasta with tomato sauce may not be on the menu but a restaurant will nearly always be willing to cook one for kids who turn their noses up at everything else on the menu.
If you are in a large group (say four or more) then it is appreciated if you don't all order a totally different pasta. While the sauces are pre-cooked the pasta is cooked fresh and it is difficult for the restaurant if one person wants spaghetti, another fettuccine, a third rigatoni, a fourth penne and a fifth farfalle (butterfly shaped pasta). If you attempt such an order you will invariably be told that you will have a long wait!
When pizza is ordered, it is served as a primo (even if formally it is not considered as such), together with other primi. If you order a pasta or pizza and your friend has a steak you will get your pasta dish, and probably when you've finished eating the steak will arrive. If you want primo and secondo dishes to be brought at the same time you have to ask.