Arriving to Switzerland by plane: 

In Switzerland, there are two international airports:
Geneva airport and Zurich airportFrom Geneva airport to Lausanne by train: between 45-55 minutes. From Zürich airport to Lausanne by  train: about 2h30.

In Switzerland: 

Timetable and ticket prices information can be found at SBB-CFF-FFS (Geneva – Lausanne fare is approximatively 25 CHF one way trip and  Zurich – Lausanne is approximately 75 CHF one way trip. Reservations are not required on these trains, so it is possible to simply purchase a ticket at the airport).

In Lausanne: 

Lausanne public transport:
You will find information at TL: Timetable and Map. Remember that when you book your room in a hotel, a pass is typically included for unlimited Lausanne public transportation. 

Taxi service:
The phone number for the taxi services call station in Lausanne is +41 844 814 814 or +41 844 810 810 or you may hire a taxi at a local station: List of Lausanne taxi stations.