By plane, Treviso airport or Venice airport are the best. The first one is served by low cost companies (Ryanair, Transavia, Wizz, Germanwings, Blueair, Belleair), the second by both major and low cost companies.

From Treviso the best way is to take SITA direct public bus line #860 for an one hour trip.

You can also take another public bus line (ATVO) to Mestre rail station (1 hour trip); return tickets cost around 10 Euros and can be purchased online or in the arrivals lobby. Then you can reach Padova by train in about 30 minutes (take trains towards Milano or Bologna).

From Venice the best way is to use the public bus as well (SITA line #815/1). From both airports there is a shuttle taxi service too.