The easiest way to get to Versailles palace and avoid queues is to buy the ticket directly from the Château de Versailles website: it costs a bit more than the usual entrance ticket but includes return railway and metro tickets, an audioguided tour of the Chapel and Opera House, the King's and Queen's State Apartments, the Dauphin's and the Mesdames' Apartments, the Coach Museum, Trianons and all the temporary exhibitions.
However, you can get to the Palace easily by train and buy tickets for each attraction once there. This may be the best approach if you want to see something in particular or just want to explore the enormous gardens.
By bike
It's a nice bike ride from Paris via Bois de Bologne and Parc St Cloud. (http://www.mapmyride.com/...)
By bus
Route 171 travels between Pont de Sèvres at the end of Métro line 9 to Versailles. The bus journey from the station to the château takes approximately 30 min.