I am trying to find the best way to go from Mennaggio, Italy to Salzburg, Austria next week - mid September. I have two days, but would rather do it in one if that is possible.
Take a bus from Menaggio to Lugano. The bus takes less than one hour. This is the schedule: http://www.sptlinea.it/Portals/5/Documents/Orari/I1213/lago/linea%2012.pdf The bus stops a distance from the station in Lugano, so you might need a taxi to the train station. From Lugano train station there are several train options with duration times ranging from 8 to 10 hrs approximately. Some have one change only (in Zurich). Do a search from Lugano to Salzburg Hbf: http://www.bahn.com/i/view/USA/en/index.shtml If you take the 7:25 am bus from Menaggio, you can be in Salzburg by 6 pm.
10 and 1/2 hours is not too bad. Another native is to take the boat to Varenna across the lake. From Varenna you can take a train. The train itinerary would be VARENNA > MILANO C. > VERONA PN > INNSBRUCK > SALZBURG. So in this last case you would change train in Milan, Verona and Innsbruck. For example you could take the boat leaving Menaggio at 6:40am and arrive in Varenna at 6:55. At 7:37 am there is a train to Milan which gets there one hour later. Perfectly on time to depart from Milan at 9:05, and after a change in Verona and one in Innsbruck, be in Salzburg just after 5pm. You still need at least 10.5 hours either way. So you choose. Anything faster you would need to go to Milan Malpensa airport and take a flight to Munich, then the train. A little bit faster, but still a few hours away once you consider transfers and airport security procedures.
Find schedules on the German Rail (Bahn) website. Your big problem is that Mennaggio is so isolated. No flights from anywhere near. It looks like the only way out are buses, one at 12:45, one 15:05. If you leave on the 12:45 bus, the fastest connection has 4 changes and ends with a EuroNight train (EN) from Munich to Salzburg at 1:18 AM. You don't spend enough time on the night train to make it worthwhile having anything other than a seat. That connection has changes in St. Moritz, Chur, St. Margrethen, and Munich. You might want to stop for the night at one of these places. The 15:05 connection has changes in Lugano and Zürich, and the night train from Zürich gets into Salzburg early in the morning. It might be worth a sleeping compartment on the train.