First take a shuttle bus to Federal Railways Station in Lugano.
From there you can take a train to Como S. Giovanni, either directly or changing at Chiasso (depending on the departure time). The direct train takes forty six minutes, while a change at Chiasso adds another five or six minutes.
From Como S. Giovanni, you can take the C10 bus to all destinations along the west side of the lake, and round as far as Colico. You can also catch the C30 to Bellagio. For fares, journey times and timetables, see Lake Como buses – timetables and tariffs.
To get to the east side of the lake take a train from Lugano to Monza, then change to the Sondrio or Tirano train for Lecco, Mandello del Lario, Varenna, Bellano or Colico. There are also trains between Lecco and Colico, which stop at less well known stations along the east side of the lake.
After you buy a train ticket, you have to insert it into one of the yellow boxes on the platform, which prints the date and time on it. This is something the inspector onboard the train will check for. Failure to do it may result in a heavy fine.
It must also be feasible to take the C12 bus from Lugano to Menaggio, then a ferry across the lake to Varenna. But the C12 starts from a spot in Lugano away from the town centre or bus depot.
Search for Hotels near Lugano – Agno airport
Read about airport taxis in [post=125]