The nearest airports serving Lugano are Milano Malpensa Airport (MXP) and Zurich Airport (ZRH). Both airports are well-connected to Lugano by train.
From Zurich Airport: take any train to Zurich main station, where you change to a train to Lugano (every half an hour, enjoyable 2hrs 15 mins trip through beautiful scenery and the longest tunnel in the world).
From Malpensa Airport (MXP): hourly train to Lugano Station (1hrs 35 mins). Note that Malpensa is in Italy so there might be an additional customs check.
For train info and online ticket sales, consider: https://sbb.ch. In case you wish to come by car, please note that you need a toll sticker (now also available in electronic version) in order to use Swiss motorways. Please consider the official website for information and official vendors (note that there are scam websites which may overcharge you!): Motorway charge (vignette) Official Website