From Paris CDG Airport:
Lyon can be reached very easily from Paris Airport, the average journey time is of 2 hours. The train departs from Paris CDG train station which is connected to Paris' main airport. It arrives at Lyon Part Dieu which is a stone's throw from the city centre.
More info at oui.sncf website.
From Lyon St Exupéry Airport:
Most international flights arrive at Lyon St Exupéry located 27 km from downtown Lyon. The Rhônexpress is tram shuttle service that goes between Lyon-Saint Exupéry airport and Lyon’s Part-Dieu train station. The tram stop can be found in the St Exupery train station.
The shuttle runs every 15 minutes, and will take around 30 minutes.Full-price tickets cost €16.10/€27.80, with cheaper rates if you buy online.
Lyon Part-Dieu is the primary railway station in Lyon, with connections to the French (SNCF) and international rail networks. It has direct access to the Lyon Metro (line B) and tramways T1, T3, and T4.
By taxi, the journey from the airport to the city center takes around 30 minutes depending on the traffic. The taxi ranks are located in front of Terminal 1 and 2. The taxi journey from the airport to the center of Lyon costs €50-60.