The Senate just voted for cloture, which in essence kills debate for the bill. They are rumoured to vote on it in its final form on Christmas Eve.
Since the bill has already been through the House, a final vote in the Senate means it is on the President's desk. If it was amended in the Senate (it was, a 300-page amendment was added hours before the cloture vote, and hasn't even been shared with the Republicans yet), it goes through a conference committee first to reconcile the different versions, and both houses must approve their changes.
After that, Obama will sign the bill, we pay taxes for four years, and it goes into effect in 2013.