Halo 2's story will be that of a continuance of the first installment. Bungie has not leaked any information on the real story of Halo 2, but we can assure you it will have a few new twists that you certainly won't expect. And we can also infer that the Covenant will find and attempt to annihilate Earth and all of its life forms. The full story is being closely guarded by Bungie.
Halo 2's story, or campaign, will continue to follow the battles of the Master Chief (aka John, Spartan-117), the United Nations Space Command, and the struggles on Earth that arise when the Covenant learn the coordinates of Earth.
Since we don't want to give out the details between how the Master Chief and Cortana get back to Earth after single-handedly destroying Halo and the Flood, along with a whole Covenant armada, and the beginnings of Halo 2's story, we suggest that you read Halo: First Strike by Eric Nylund.
You can keep track of the production of Halo 2 by following the weekly updates done by Bungie's own Frank O'Connor (or Frankie for short). Starting since the announcement of the production of Halo 2, Bungie has been giving updates every Friday which include technical details, multiplayer details, etc. Bungie has been very secretive with the official campaign story, and haven't released any information on the storyline. So far there are about 40 updates. Check out our Bungie Weekly Update Archive.