How do we get from Venice to Varenna fast, cheap, and easy? Is it possible?

You can use trenitalia.com to find the train schedules, making sure you use the proper place names in Italian even after you change the site to English (i.e. Venezia Santa Lucia for Venice). You can buy in advance, sometimes there are huge discounts although I dont see any for this particular route, so you may as well wait in case it takes longer to get to the train station than you thought. Looks like it costs about 45-65 euros per ticket, trains leave every 30-60 minutes, and you will have to change trains in Milan. It takes 4-5 hours.

If you do buy in advance, I believe you can only buy a few months in advance. Summer schedules might not even be posted this early, so use a date and time within the next few weeks similar to what you plan to do.

Thank you! The two pieces of information that really helped me are to use the correct Italian name for the city--even on the English site. Previously when I put in Venice..... of course, it told me no such train station. Also I did not know we had to go through Milan to get to Varenna. RS gives excellent info about the Milan station and lots of details about the trip from there. So when I put in the correct name I got some information. Now I need to figure out how to use the train's web site to book a ticket. It's very confusing. Can I just but the ticket in Italy or might the trains be full of tourists if I wait? There are 4 adults who need tickets.

Look Sharon. I've lived in Italy the first 27 years of my life and go there once a year at least. I've traveled by train more than I can recall, yet I've never pre-purchased tickets. I've always walked inside the station and bought the ticket on the spot at the ticket window or the automatic kiosk just minutes before departing. In the many thousand times I've done this, never have I seen a train where all seats were sold out. At most the second class was sold out (maybe a couple of times between Florence and Rome) in which case I either bought the higher class ticket, or simply waited for the next train half hour later, which always had second class seats.

In your case, the leg from Milan to Varenna will be on a regional commuter train, therefore you can't purchase ahead and there are no discounts for doing so.
You could purchase ahead the Venice to Milan leg on a Frecciabianca (up to 4 months ahead) and you might be able to secure a discounted fare in that case (called Supereconomy or Economy). However be aware that if you miss the specific train you book when you purchase a discounted fare, the ticket becomes null and you must buy another ticket at the full 'base' price. Since you can't be sure of the time you can be at the station, since the cruise ship might be late and the disembarking might take time, I would simply purchase on the spot when you walk to the station. You will find plenty of empty seats to Milan. Who in their right mind would want to go to Milan on a Saturday in the middle of scorching July? If anything there will be lots of people trying to get out of Milan as fast as they can to hit the beaches. Probably just the four of you and few other tourists headed to the lakes will be on that train to Milan. There might be more people from Varenna to Milan, but regional trains are like subways, as long as you can squeeze inside the cars, there is room, sometimes standing only. Since you will be in Milan past the morning rush however, that train will be half empty as well.
Don't forget to stamp you tickets before getting on the regional train or they give you a fine. The stamping machines are on the platforms. You have 6 hours to complete the trip from Milan to Varenna from the moment you stamp the ticket. The trip is only 1 hr.

Actually Kent, traveling with public transportation in Italy is generally cheap, easy and fast. It certainly is between Venezia and Milan or even Varenna. Think about it, you can go from Milan to Rome in just over 2.5 hours, city center to city center, for under $100 one way (full base price!) on a train or even half that on a super economy ticket. To cover the same distance from San Francisco to L.A. if I take the train (Amtrak) it takes me 13 hours and it costs me even more. Driving takes 6 hours with no traffic, and it's tiring too. If I take the plane when I include the time it takes to go to/from airport, and the time it takes to check in, be stripped and groped by TSA, and board, it takes me at least 4 hours to get to LA. I think travel in the US is the one that is not cheap, not easy, and not fast.

Good info. Thank you. Another question... How long is the train ride from Venezia S. L. to Milan? Any ideas on how to get from the port of San Basillio to the Venezia train station? And how long might that take? I love it that some of you actually know how to make all these connections.

Venezia S.L. To Milano Centrale is 2.75 hours by train. From there to Varenna is 1 hour 3 minutes. You will need to add some wait time between trains, but it should not be long.

Roberto,
That's why I deleted my post, because I realized I was wrong, in just the way you pointed out.
Appreciate the correction.

I'm not 100% positive where the pier is, but Venice is quite small and you can walk just about anywhere in a short amount of time, or take the Vaporetto (Venices water "buses"). I know there are some cruise ships that dock not too far from the train station (or Ferrovia in Italian), but I dont know if that is where you will be. I'm sure there will be lots of people disembarking at the same time and quite a lot of them will be heading to the same place as you. I'm positive there will even be people from the ship directing everyone where they need to go. There will probably even be some signs every few streets directing you towards "Ferrovia". Really, you will probably be fine.

Rome2Rio.com says that San Basilio is a 5-minute taxi ride to Venezia Santa Lucia station, or about a 15-minute walk.

There is a people mover from the Cruise port to Piazzale Roma. Then from there to the station is a 5 min walk.

San Basilio is separate from the main Marittima cruise terminal. It is at the west end of Fondamenta Zàttere, in Dorsoduro. I don't know if they can access the People Mover from there. There is a vaporetto stop near San Basilio and they could take that to the Ferrovia stop for the train. Much easier with luggage than getting to Piazzale Roma and walking over the bridge.

restrooms in the Milan are down some stairs and seemingly a half mile walk.....and each person needs a euro coin to go thru the turn stile to get into the restrooms. word to the wise.
toilets on the train might not be pristine, but much easier, cheaper, faster, closer.