By Train

The nearest railway station is the one at Terme Euganee - Montegrotto, on the Bologna-Padua line, all the main trains stop here.
Other wise just as convenient is Padua station, on the Milan-Venice line where all the trains stop. Then from the square right in front of the station buses leave direct to Abano every 15 minutes, the bus lines are A, M, T or AT and the journey takes 30 minutes.
Both of the stations have a taxi service.

By Airplane

Arriving in Abano by air, the nearest airport is that of Venice (60km) where most of the main national and international companies land. From here you can get to Abano by taxi or on a direct bus line, Airport-Abano (this takes 1h 30min).
There are also international airports in Treviso (70 km) and Verona (80 km), both are not far from Abano and are easily reached.