The vast majority of visitors fly into Los Angeles International (LAX), then hire a car or have a driver take them up the coast, a journey of around an hour if the traffic is light.
Trains
There aren’t any convenient stops for Malibu, so you’re much better off driving or taking a cab.
Automobiles
They say the car is king in LA, and Malibu isn’t really any different. The city is spread along the coast and has no real centre, so it’s not particularly well laid out for walking.