By train :

The Vernon station is situated on the main line Paris / Rouen / Le Havre. It starts from the Saint-Lazare Paris station (which has not changed much since Monet painted it). The fastest trains complete the journey in less than 45 min.

In the Metro, take the 'SNCF - Grandes Lignes' exit. Buy a ticket to Vernon. The Rouen line departs from the right side of the platform, in the 'Grandes Lignes' section.

By road :

Vernon is 75 km from Paris. Leave Paris by the Pont de Saint-Cloud and take the highway A13 (towards Rouen) for 55 km until you reach exit 14 (Bonnières) or exit 16 (Douains). The A13 is free until Mantes-la-Jolie. The charge is 1.80 euros to go further. After the exit follow Vernon or Giverny signs.
You may also leave the highway before the tollgate (follow green Vernon road signs) and go on the N15 past Rosny, Rolleboise and Bonnières. The road follows the River Seine for a while.