I haven't re-read this thread so I'm not sure whether it has been mentioned--and you probably already know this--but you'll save money on any fast trains you plan to take if you can pin down your schedule and buy those tickets in advance. Even if it's just one or two travel legs near the beginning or end of your trip, there are savings to be had.
Buses are virtually always cheaper than trains for last-minute purchases; they are often quite a bit slower, but it's worth checking both schedules.
When buying train tickets, look carefully at travel times. For trips to or from a smaller city, you'll need to spend some time on a regional train. Sometimes a trip that is all-regional takes no more time than a trip combining a regional train and a fast train, because the layover may eat up any time you gain on the fast train. Any all-regional ticket will be cheaper than a ticket with a fast-train segment.
Stopping in a bar/café for a cold drink is relatively cheap if you consume the beverage while standing at the bar. If you sit down, the price is likely to double or triple. Similarly, ice cream bought at a take-away counter is far, far cheaper than ice-cream at a café table. The cheapest source for cold beverages will usually be a small grocery store, but those are not always convenient, and if you're hot and parched, the bars are not too costly. I carry a water bottle around with me so I don't have to buy multiple bottles of water each day. There are often public fountains scattered around where you can re-fill your bottle. Don't do this at the larger decorative fountains, of course.
You will find it probably not so easy to avoid paying for water (if that's your beverage of choice) in restaurants. You can try to get tap water, but it's a cultural thing. At least the bottled water will usually be cold. Do be sure you make it clear whether you want still water or bubbly water. The bubbly kind is the default in Italy, and I have sometimes been served that even though I specified still water. Always look at the label on the bottle before drinking it. You don't want to pay $4 for something you don't like.
Cooked-to-order pizza (i.e., a full pizza from a pizzeria, not a slice cut from a slab sitting on a bakery counter) is almost certain to be better than any you have had in the US, and it is typically less expensive than other hot options in Italian restaurants.
I check my suitcase on the plane, so I carry a small paring knife with me, to be used for slicing bread, cheese, tomatoes, etc. One meal a day in a restaurant and one meal that's put together at a market is my goal.
Not a cost issue, but: Don't touch the produce! You are supposed to indicate to the market-stall holder what you want, not paw through the merchandise.
If you're willing to stay in a hotel room with the toilet and shower down the hall, you can save money, though there aren't as many rooms without en-suite baths as there used to be. I would not cheap out on air conditioning, though. You may very well need it.
Postage back to the US/Canada is very expensive, even for postcards. Don't promise to send people cards!
