Can we use our Eurail? Which Paris station do we depart from to travel to Versailles? How do we get from station to the Chateau?
That would be an absolutely waste of one day of a pass.
You take the RER C train from several locations in Paris. Be sure to take it to the Versailles Rive Gauche station. From there you walk 5 minutes to the Chateau.
Your pass won't be good on the RER C. Besides, the fare by metro and RER from anywhere in central Paris is only €3.05 each way. The RER C divides on the west side of Paris. Be sure to get on a train that is going to Versailles-Rive Gauche. Those trains have the nameplate VICK.
Everything you need to know about the journey you can find in your copy of Rick Steves' Paris. You can get hints of what to do when you get there too, and ways to save money.
Elizabeth, ditto the above posts. There are also large signs pointing you to the chateau once you exit the station. You will need Rick's guide to help you find your way around.
There are tour offices on the walk from the station to the entrance gates, which may try to talk you into a guided tour, in order to avoid waiting in lines. That's your call as to whether it makes sense for you.