Genève-Cointrin is the nearest airport. By train, it takes ~45 minutes to reach Lausanne. Zürich Airport is about ~2.5 hours away by train.
From Lausanne, you can take the metro. You can take the M2 line (direction Croisettes) from the train station one stop to “Lausanne-Flon” and then the M1 line (direction Renens) 9 stops to “EPFL”. Metro tickets can be purchased from the machines in the station. For more information, see the metro website.