In order to look for pricing or reservations, use the instructions below.
For example, let's look at Venice to Verona.
1. Go to the official website at
http://www.trenitalia.com/en/index.html (or .../it/... for the Italian version) - NOTE: this is a recent change...www.trenitalia.com goes to a new page now that is only in Italian.
2. Click on English on the upper right (if it's not in English already)
3. Enter "Venice" as the starting point and "Verona" as the destination.
4. Choose a date that is within 60 days and is the same day of the week as when you want to go - train schedules don't change that much over the year. You do this because prices are not available farther out, so this process won't work.
5. Choose a time a little before the best time for you to leave (or choose 6:00 a.m. if you don't care).
5.5 In this particular case, the website will wonder which station you want in Verona. I don't know why it can handle multiple stations in Venice and other places but not Verona...oh well, choose "Porta Nuova" (the main station).
6. You will get the first 5 solutions in terms of departure time. For additional solutions, click on "Other options" - lower right. This will give you 5 more trains immediately following the five you see. You can click through the day's schedule by clicking on Other options and Previous options.
7. Pick the IC train (InterCity) that leaves at 06:51 (get used to 24 hour time, all railroad schedules in Europe use it).
8. When you want to price a train, click on the shopping cart icon in the far right column (under "Buy") of the train you want to price. In order to get a price, you will need to choose a fare (the pull down menu that says "Choose your rate"). Choose "Standard", which is what we tourists will normally pay. Then the screen will refresh and by default give you the first and second class fares for 1 adult.
9. When the screen refreshes with the fare, note the new pull down menu that appears in the section marked "Seats descriptions" under "SERVICES PREFERENCES" (i.e., the next section after "Fares"). Click on the arrowhead; you will see two choices: "Mandatory reservation" and "Seats". The presence of both phrases means that there are both reservable and non-reservable seats on this train.
10. Note the Back and Next in the lower left part of the page. These buttons take you to the previous or next trains (not obvious). Click on "Next".
11. You are now looking at the regional train (R) that leaves at 07:09. Look at the pull down list under "Seats Descriptions" - it says "2nd class seats only" - that is, there are no reserved seats on this train (nor first class either).
After doing this for a while, you will see that the regional trains (R and iR) tend to have no reserved seats, the Eurostar and other fast or international trains often require reservations for all seats, and the inbetween trains like the InterCity trains may have both (or may not).
So, for Venice to Verona, the answer is, "some trains do and some trains don't", but now you can see which ones do.
As for Verona - Sorrento, well, now you have a totally different set of issues.
1. Trenitalia doesn't service Sorrento - you have to go to Naples and change train systems to the Circumvesuviana...not really a problem, but the trenitalia website isn't going to give you a solution all the way.
2. Don't worry about "Bologna"; I think every train from Verona to Naples probably changes in Bologna.
3. Because you will change trains in Bologna and possible Rome, you are likely to be on several different trains of different types.
4. HOWEVER, note that the website gives you "solutions", not complete timetables. Thus, you may find it possible to take regional trains all the way, but have trouble with the website telling you this unless you figure out how to ask it...but that would make this note too long...
By a fluke I found a way to see timetables buried in the website - see http://forum.virtualtourist.com/discussion-334317-1-1-Travel-0-51-Italy-discussion.html.