The eighth General Congregation of the College of Cardinals has decided that the Conclave will begin on Tuesday, 12 March 2013. A “pro eligendo Romano Pontifice” (Latin for "For the election of the Roman Pontiff") Mass will be celebrated in St. Peter’s Basilica that morning. In the afternoon, the cardinals will enter into the Conclave.
In the meantime, please consider going to the Adopt-a-Cardinal website. There you may register to be assigned one of the 115 voting cardinals to pray for. How you choose to pray for the cardinal who will be voting for (or possibly be elected) the next pope is up to you. You may wish to pray a rosary, fast, or gives alms or some other form of abstinence, before and during (and maybe even continuing after) the Conclave.
(I already signed-up and was assigned Cardinal Laurent Monsengwo Pasinya, Archbishop of Kinshasa, of the Democratic Republic of Congo,formerly Zaire.)
Remember, it is important to pray for our cardinals and the next pope. Even though nothing happens without God's allowing it, that is not the same as his preferring it.