Public transit in Italy

Not quite.
If you are talking about train travel (and not buses), read this page: http://seat61.com/Italy.htm
There are two types of trains, with different rules:
1) Regionale (local trains). Here you cannot book in advance. You buy a ticket (either on the day or before), and it is valid for any train on any day. With this ticket you have to stamp it (with the date and time) before you get on the train. This is to stop you using the same ticket twice.
2) Long distance trains, including high speed trains. Here you must book, either in advance or on the day. When you buy your ticket it is for a specifiy train on a specifiy day. On the ticket it says date, time, train number and your coach and seat number. If you book in advance (up to 120 days) you can get a deep discount, but once you have booked you cannot change your mind and get a refund. If you miss the train, hard luck, the ticket is only valid on that train (like air tickets).

RonInRome.com covers all types of transport in Italy.

if you pre book specific train time to travel and miss the train you
are out that money.

Connie, that isn't necessarily true. It can depend on what sort of ticket you purchased on what sort of train. For instance, on Trenitalia, a base-priced ticket can be changed, for free, if you miss that train but you can't do that on a super-economy ticket. This may be helpful?

http://www.trenitalia.com/cms-file/html/frecciarossa_en/Info_Tariffe_en_LeFrecce.html#BASE

This is also a great resource for train travel in Italy:

http://www.seat61.com/Italy-trains.htm#.Vrs7Hkuwg4Y

I understand getting train ticket validated before you get on train(
you get a penalty which isn't cheap)

You don't have to do this if your ticket is for a specific train/time for which you have seat assignment numbers. Validation is necessary on regionale or local commuter trains which have no seat assignments. These are the cheapest types of trains, and there's no price break/advantage for buying tickets in advance on the website like there can be for the more expensive fast trains. They're also slower and make more stops but you will find that you'll use them quite often if doing short day trips. Tickets for these trains are good for two months after date of purchase so if we're doing a day trip which has us using a regionale both directions, we'll just buy both tickets at the same time: they're good for up to two months so we can validate and hop on a regionale going back whenever we're ready to go. There are no seat assignments so sit anywhere.

If you have a ticket that's specifically for a 1st or 2nd-class carriage, look for numbers 1 and 2 on the outside of the carriages. Carriage numbers - if your ticket is specific for those - will be on the outside as well.

@Chris: In trying to make reservations in advance (using trenitalia) I am finding that certain routes are available while certain routes not. E.g. I was able to book tickets from Milan to Vernazza (about 110 days in advance), but am unable to buy tickets for travel from Vernazza to Bolzano for May 31st. On trenitalia the checkout cart is dimmed and crossed out even though that journey is less than 120 days away. Does it have to do with the fact that Milan to Vernazza involved Intercity and Vernazza to Bolzanno involve Frecciabianca and/or Frecciargento. Does the advance booking window vary depending on type of train? Perhaps I should pose this question on a different/new thread...

For buses, you buy your ticket from a newsstand, machine at major bus stops (Piazza Venezia and Piazza San Giovanni in Laterano come to mind), or sometimes tabacchaio the latter will have a "T" sign outside). You must then validate your bus ticket in the box near the driver or at the back of the bus; some buses have a validation box in the middle of the bus as well.
A few buses have machines that accept coins for purchasing tickets onboard, but I would not count on it.

For trains, if for some reason your ticket cannot be validated because the machine is broken (always check your ticket for a tiny date/time stamp), find the conductor before he/she finds you and explain the problem, he/she will hand-validate your ticket.

Only regionale train tickets need to be validated (green/white/red machines near the tracks, in the tunnel leading to the track stairs, or in the station). Do not validate them day(s) in advance of your travel date, the conductor will consider them used and therefore invalid.

Vishal, I see tickets available on trenitalia.com from Vernazza to Bolzano - Bozen for 61.80 euro. Are you sure you are choosing the correct station name?

Connie, another thing to look for is that some cities have more than one train station with similar names. Be sure you are choosing the correct one (when in doubt, your hotel can probably advise you, or post the question here).

Connie,

A bit of clarification......

• Tickets only need to be validated for Regionale trains. You also need to validate tickets for Metro, Buses, and other forms of public transit. Tickets for the high speed trains do not need to be validated, since they're specific to a particular train, date and departure time.
• The fines are indeed "not cheap". THIS photo provides more information on that.
• As you've noted, tickets for the Freccia and InterCity trains are specific to one train, date and departure time. If you miss that train, your ticket can NOT be used. If you board the wrong train by mistake, you'll be deemed to be travelling without a valid reservation and, you guessed it, will be fined on the spot! In that case you'll not only have to pay the fine, but also the cost of the reservation which is currently about €8-10 PP, depending on which type of train you're using.
• A few points regarding the tickets for the fast trains. Many travellers like to purchase tickets in advance to take advantage of the discounts. If you purchase the cheapest Super Economy tickets, these are non-refundable and non-changeable once purchased. If you buy the somewhat cheaper Economy tickets, these have very limited change provisions, and a fee is charged for changes. If you buy the full fare Base tickets, these have more flexible change provisions. However even if you buy one of the tickets which allows changes, you'll need to be aware of the practicality of exchanging your tickets. This will require a visit to a staffed ticket office, and in many of the larger stations these often have a LONG queue that zig-zags for what appears to be a kilometere. If you're willing to stand in a queue for an indeterminate length of time, then exchanging tickets is certainly an option. In a few cases when I've had to deal with queues for the ticket windows, I've had the misfortune to be behind people that have enormously complicated situations to resolve, which can sometimes take 20 minutes or more.

Yesterday night Trenitalia's booking system crashed and they are slowly loading all trains in the system again.
That's the reason why some trains display the barred cart instead of prices even if you chose a date within the 120 days limit.

The general rule about validation is very simple: you have to do it only for regional trains tickets NOT purchased online.

Thank you all for such great advice and links to check out!!!!