Via airplane: Arrive to Lyon Saint-Exupery Airport (LYS) (and not to Grenoble airport): this possibly implies flying to Paris CDG and, from there, to Lyon.
Once arrived at the airport, get the bus to Grenoble Gare routiere (=train station), which leaves every 30min or 1hr and brings you to the Grenoble central train station in 1 hr. Please buy the ticket in advance at the following site:
In case your flight is late, they you can get in the next bus without problem.
Via train: This is the easiest, fastest and more ecologically way to reach Grenoble from most of Europe. There are various possibilities:
From Nord Europe: the TGV (Train Grand Vitesse) from Paris Gare Lyon to Grenoble central station.
From South-East Europe: the TGV (Train Grand Vitesse) from Milan/Turin arrives to Chambery and then from there the local train Chambery-Grenoble central station (there are frequent trains).
From South-Ouest France: the TGV (Train Grand Vitesse) from Barcelona/Toulouse/Marseille to Valence Gare TGV and then from there the local train Valence-Grenoble central station (there are frequent trains).