How to get from Salzburg to Varenna, Italy?

For most departure times and for the fewest connections you will need to go via Milan. See the detailed timetables on the Swiss Rail site. Enter Varenna-Esino as your arrival point.

Because of the rugged terrain in eastern Switzerland and the Alto Adige of Italy, there are not many train lines through the area. There are a few roads and buses. It's been a while, and I don't remember exact details, but I once looked at getting from Varenna to Innsbruck. It seemed you could get from Varenna to the St. Moritz area by train and then from there to the Tirol by bus, but, unless you just wanted a close look at that area, it would be faster to go to Milan, then to Verona, then to Innsbruck.

Yes, go to Milan Centrale and catch the train up to Varenna. You could take a train to Como and from there take a ferry, but time-wise it will be about the same. I think, if you are adventurous and have time you can take the train to Bolzano and from there get to Varenna as well. If you want to break it up a little take the train to Feldkirch do an overnight there and catch the train in the morning that takes you to Chur and from there you catch the postbus to Bellinzona to get the train to Milano Centrale or Como. Swiis rail site is good for the various routes. You will love Varenna. We are planning to move there.

There is a way to do this without going to Milan. Salzburg>Tirano then change to Trenord to Varenna. This doesn't show up because Trenord schedules do not show up on International Train Schedules. Perhaps Trenord does not want to pay booking fees to other networks. The schedule through Milan is definitely faster, but not excessively so. No idea about cost, and SBB can only quote until next day. Here it is. Via Milan: 10:53>20.23, 9.5 hours (fastest connection of the day, 3 changes) Via Tirano: 8:02>20.36, 12.5 hours, but includes 1.75 hour change in Tirano (enough time for dinner)
So if you want to spend more time on alpine trains, it is doable. If you just want to get there ASAP, go via Milan. The Tirano route goes thru Arlberg tunnel to Sargans, change to Chur, change to St Moritz, change to Tirano.

Wow - thank you all so much for your detailed replies! If we go Salzburg/Milano/Varenna, what is the scenery like? I can only assume it's gorgeous, but if we're going to be on a train that long, I wanted to double-check that there will be plenty to look at! I should mention too that we will be traveling in early November.

At Verona you will exit the Adige valley. The stretch from Verona to Milano (1.5 hours) I would characterize as Peoria to Chicago. 20 minutes after departing Milano, you leave the industrial suburbs behind and enter lake district, but it will be dark by then.

I just went to the Swiss Rail site and entered an arbitrary date in early November. It shows a route leaving Salzburg at 08:02 and arriving in Varenna-Esino at 18:36 (not 20:36). Tirano is not on the route at all. The leg between St. Moritz and Chiavenna is on a bus. For a different route you could leave Salzburg at 06:53 and arrive in Varenna-Esino at 17:23. Sunset in early November will be around 17:00. The Swiss Rail site shows maps of the routes which might help you decide which one to take.

Yes, as was pointed out recently, the ever efficient Swiss show the most efficient route, thus they advise taking the bus from St Moritz to Chiavenna over the Maloja Pass. The Bernina Express train just misses the connection at Tirano with the train that gets to Varenna at 18:36, thus the hour and 47 minute change at Tirano. The route with the bus has an additional train change at Colico.