In a restaurant there's only one way to prepare coffee in Italy. It's not a good idea to ask for espresso in Italy. Everyone will know what you mean if you do, but that's not what it's called. It’s just called coffee, or in Italian, caffe'.

There are a lot of different ways to brew a cup of coffee; drip, french press, moka, espresso, cold brew, instant coffee, single-serve Nespresso, and so on. Espresso is just one way of brewing coffee. The only way coffee is brewed in a bar or restaurant in Italy is espresso. In your house you have other options, where it takes 5 minutes to brew a cup, but not in a restaurant. In the USA the predominant way is the "drip" method. Hot water is dripped over ground coffee beans. You don't enter a diner in the USA and ask the waiter for a "drip," because that's the only way they make it. As in Italy, you just ask for coffee

There are situations where it makes sense to ask for espresso, namely, when you are in some countries outside of Italy. In the USA an Italian restaurant will serve drip coffee, and also have an espresso machine. The waiter will ask, “Would you prefer regular coffee or espresso?” In places like Starbucks you can specify that you want you coffee brewed by drip or espresso method. In Italy the bartender will not ask, "would you like the coffee made in an espresso machine, or would you like us to use a drip coffee maker?"

Once they brew the coffee you can tell them what you want them to do it with. Most people say, “normale,” which normal, or as it is. Some find “normale” to be too bitter, and ask for a "macchiato," which means stained with a teaspoon of steamed milk on top. A few ask for caffe' lungo (long coffee), which means dilute it with a little bit of hot water. Some ask for caffe' americano, which means pour the shot into 1/3rd of a liter of hot water and serve it in a large cup.

Some ask for a cappuccino, where they pour half of a cup of creamy, foamed, steamed milk on top of the coffee. Because of all of the heavy milk, a cappuccino alone often counts for breakfast, unless you are very hungry and have a croissant too.nYou can ask them to put the shot of coffee over ice, to add chocolate, cinnamon, to pour the shot into a glass of milk, to make it "coretto," which means to add 1/4 of a shot of whatever type of liquor you want it "corrected" with (grappa, vodka, whiskey, cognac, brandy, etc).

Every waiter in Italy will understand you if you ask for an espresso, but it doesn’t sound right. It isn't wrong, but it isn't "normale."