I read that Pope Benedict XVI is resigning. I don't know much about Catholic/papal authority as it relates to leading the Church, but as far as I can remember, a pope dies before another one takes the reigns. Apparently, this has happened before, but how does the living pope confer that authority to a successor, since he's still alive? Since he resigned, is his authority to lead the Catholic church removed from him, or how does that work?
Yes, as the Pope said in his resignation speech, he gives up the office and it is for those whose duty it is to convoke the conclave and elect a successor — just as it would be if he had died.
As a cardinal, he's entitled to attend the conclave (but he probably won't) but he can't vote because he's over eighty.
Pope Benedict may follow the pattern of previously resigned popes and spend the rest of his days in a monastery. Alternately, he may live quietly with his brother. Either way, he will do his best to stay out of the public eye so as to give his successor the freest hand possible. (This is the same thing that usually happens when a U.S. president leaves office; it’s traditional for him to more-or-less vanish, at least for a time.)
The papal authority is removed completely from the ex-pope. From wikipedia, I understood that his ring, seal etc. are destroyed as though he died, though it's not clearly stated there.
As Andrew Leach wrote, as a cardinal the ex-pope can attend conclave, but even if he was younger than eighty, he would be expected not to be very active in the election of his successor (part of the tradition of vanishing from public).
EDIT: according to what I found while researching answer for a related question, there is an aspect of the pope's role he maintains after resignation, or even after death: the obligation and authority to pray for the Church.
Another EDIT: as Cardinal Lombardi said, Joseph Ratzinger won't participate in the conclave. In Czech version the Vatican Radio goes to more details, such as that Ratzinger will no longer be a Cardinal, but I didn't find it in English.