Internet in Europe?

Internet - no difference. Your device (computer, Ipad, phone) will show available Wi-Fi choices just the same as it does in US. Just pick one and use just as you would here. If you are also asking about phone calls or texting, that is much more complicated depending on your phone and your US carrier; I'll let someone else advise on that; or you can search here for many other posts on the topic. Enjoy your trip!

Are you using a US phone provider's international plan in Italy, or what? See the link under Travel Tips on menu on the left.
Wifi widely available, and at most hotels.

I use only Wi-Fi in Europe, and that has not required that I do anything special on either my smartphone or tablet, both of which are Android. I haven't tried to use a European SIM for internet connectivity.

Wi-Fi quality in hotels varies as to speed; I can't vouch for its usability for something like streaming video. Occasionally there are reliability issues when the lodging seems not to have enough bandwidth for the number of rooms, in which case service can be spotty in the evenings when more people are online. That has been quite unusual in my experience, but I pay attention to comments about Wi-Fi quality in the many hotel reviews I read before making a reservation. I'm sure that helps me screen out the places with the most problematic service. I also mention, when booking, that good Wi-Fi connectivity is important to me; that's in hopes of being assigned a room relatively near a router.

Some restaurants, train/bus stations, and intercity trains/buses also have Wi-Fi, and there are public hotspots in some cities. Public Wi-Fi can be flakier, so the only place I assume I'll be able to connect is my hotel. In England I've encountered a few restaurants whose procedures is to text a confirmation code to your cellphone that is needed to complete your Wi-Fi registration. That obviously doesn't work if you do not have cellphone service.

Works the same.

If accessing internet via cellular data (with your phone) your mobile phone provider will charge you for international data roaming charges, which can be very expensive.

If you have an unlocked phone, it might be a good idea to buy a local SIM card to use while there.

You can also subscribe to an international plan with your provider, but it is not as cheap as an Italian SIM card (but cheaper than no plan at all).

Unless you buy a Data Plan for your device while you are in Europe, you should know that using data on the internet, (for example, looking up directions or an address on your phone while you’re out and about,) will cost you a lot of money. However, using WiFi in your hotel, at an attraction, etc., where WiFi is available, will be not run up data charges on your phone. To avoid incurring data expenses, keep your phone on airplane mode. This will not prevent you from using it for WiFi.

All correct above - basically, the internet the same. That's why they call it the World Wide Web. ;)

One minor potential item to be aware of: non-US keyboards often have the physical key layout slightly different from what you're used to - especially in places where the native language uses different characters. Keyboards (real and virtual) on your own devices obviously won't be any different. But if you're using a shared computer, that keyboard might be different.

Not an issue at all in English speaking countries, and only a few minor changes in other countries that use some different (accented) characters. Once you venture off to someplace where the "Roman" characters (the letters A-Z, etc.) are not the primary character set, then it gets more interesting - if you're off to somewhere in eastern Europe or elsewhere that uses Cyrillic characters (Russian) it may be more challenging. In Asia, it can be much more interesting. In most all cases, you will see more (maybe lots more) characters printed on each key on the keyboard - there may be up to four characters on each key, usually printed in each corner of they keys. You typically invoke the desired key by pressing some Function key or making a choice via software for the desired keyset.

For most tourists, this will never be an issue. But if you sit down at a shared computer at a hotel or cafe in Bulgaria (or Beijing) you may have to slow down your typing and look carefully to see what's printed on the keys. Don't worry about this, just don't freak out of you go looking for the question mark or exclamation point characters ("?" and "!") and you don't see them in the usual spot. They will still be there, just somewhere else (along with various characters that are probably unfamiliar to you).

It's a big world out there. That's good. Don't let it spook you.

I'd also add this: do be a lot more careful when using a shared/public computer than you would be at home. In a small hotel (especially) or in a cafe, they are busy with primary work tasks, and setting up and maintaining a secure computing environment is not their specialty. It's not unusual to find a shared computer in a small hotel is only barely functional, a complete mess with people's personal files saved to the desktop and all sorts of trash scattered about, open browser pages with popup ads and possible links to malware, etc. I would certainly not connect a USB thumb drive or other device to that kind of unattended PC, and I'd be v-e-r-y careful about accessing your personal accounts on one (everything from a bank - I just would never do that - to cloud storage services/virtual drives, to things like gmail...just too many opportunities for bbad stuff to happen).

I too only use WiFi in Europe. Not having a data plan meets my needs. I just have to remember to turn off data roaming and turn on airplane mode! I also use WhatApp to connect with family and friends.

When we were in Ireland, we used Wi-Fi calling and paid no international fees to call home. Under settings, we switched our phone to Wi-Fi calling and as long as we were connected to the internet, we were able to make calls free of charge. The only problem was when you had very weak internet connection which happened one time. When I was on Verizon, I could just switch the cellular setting to Wi-Fi calling but on AT&T, I had to call them and have them enable it for my phone. I can now switch it whenever I need to.

Just a quick follow up after our trip. Thanks for original input. You were right, for our needs the internet worked just like using it in the US. And, both the cell service and wifi worked great too.
Stopped at a Tim Store and had them insert their Tourist Plan Sim card and within 30 minutes we were up and running. Worked just fine.

Thanks for coming back and filling us in with the way it went....

Nigel-
You are quite welcome. All the help and guidance we received really made our trip very special!
And, we are going back. Already planning our next trip.