I don't believe you can drive the whole thing. It is blocked and turned into a dirt road in some parts. But you can try it.
Look at it on google maps to plot your route. maps.google.com
If you live in Hollywood, obviously you can take the Hollywood freeway 101 exit at Barham, at get over to the Cahuenga Blvd. side, turn left heading south and you will see the east entrance (6707 Mulholland Drive) and drive from there all the way to Malibu to your pleasure. You can also check for road conditions or dial 511 on your cell.