According to the Bungie Weekly Update, the PvP area of the new expansion will be free for a week starting when the patch for the game goes live. The patch, which will update the core game along with bringing in stuff for the expansion, will release September 8th. The expansion ( The Taken King) then releases on the 15th.
The free content includes two new game modes, Rift and Mayhem. Rift is your every day capture the flag style game with a Destiny gameplay twist. Mayhem is all out war between players, but your supers will charge extremely fast, thus mayhem ensues.
The Taken King is bringing in all kinds of content to Destiny as the first true expansion. It will raise level cap to 40, unlock new features to the game, and have a new Raid 3 days after release. It also includes new story content, something Destiny is desperate for!
The update will also tackle the core game, along with the expansion. Nolan North will be the new voice of Guardian throughout the game, and some major fixes will come with it. Bungie also announced Moments of Triumph has been extended for all players.