If you want a true Cheap Eat, go to a cafeteria, snack bar, or dine al fresco with a picnic you have put together yourself. A guiding principle in Italian dining is that you eat one food at a time and that every food has its place. If you order a light supper of pasta and salad at an informal trattoria, you will be served the pasta first and the salad after. If the waiter does not bring the Parmesan cheese, it probably does not go with what you are eating. Parmesan is never used on pasta with fish or lots of garlic, but it is offered with many types of soup.
Bread is served with all Italian meals and is part of the pane e coperto charge.
Butter is seldom served except with breakfast. The container of olive oil on the table is for more than sprinkling on your salad. A plain broiled or grilled fish is enhanced with a few drops of olio, and maybe some lemon. In Venice, extend this to Monday, since the Rialto Fish market is closed that day as well. Coffee is served after a meal, never with it.