I don't know the driving time, but the direct trip via RER "C" is an easy 40 minutes or so from Paris Austerlitz station. Your destination will be Versailles Rive Gauche and the train will have the word "Vick" above the driver's window.
When you reach the station, walk down the steps to street level, turn right and walk about a block and then turn left. At the left turn, you'll see the Chateau. The walk from the station will be about 10 - 15 minutes, depending on how fast you walk.
Depending on what day you go and the time-of-year, there may be long queues to get into the Chateau, even for those with a Museum Pass. On some days, there's an extra charge for the gardens, but it's very reasonable. The gardens are HUGE, so be prepared for lots of walking (although they do offer a small "tourist train" that will take you down to the lake).