While it's not one of our usual sources for Christian views, CNN did an article discussing this, and given that this is the first retired Pope in 600 years, and the occurrence is extremely rare, their answer is actually pretty good...
His needs will still be seen to. There is no dictate as to what he should do, per Catholic doctrine, but he has indicated what he intends to do.
First, the statement that his needs will be seen to are addressed here:
The 85-year-old will first leave Rome to go to the papal seaside
retreat, Castle Gandolfo, until a successor is named. Then he will
head to the Mater Ecclesiae (Mother of the Church) building, which
formerly housed a cloistered convent in the Vatican gardens.
Later on, the article explores what he intends to do in this retreat - Devote his life to prayer:
In the chapel the pope might say Mass every day for his small
household, said Monsignor Rick Hilgartner, executive director of the
U.S. Conference of Catholic Bishops' Secretariat of Divine Worship.
Benedict has said he will devote his life to prayer. There is no
playbook for the life of prayer for a retired pope, Hilgartner said.
"Nothing beyond the normal routine" for a monk or a priest.
He said that would include "prayer throughout the day and the liturgy
of the hours, morning prayer, evening prayer, Mass every day."
As for his financial needs:
There may be a stipend for the retired pope. Italian news outlets have
reported retired clerics receive up to €2,500 a month. Hilgartner said
Benedict won't need much money if any at all. The Vatican will take
care of his lodging and his health care.
"He didn't have a pension because the presumption was he would be in
office until he died," Hilgartner said. "His needs will be cared for.
Because of the way he'll be living, those needs will be somewhat
Historically, however, for how the other Popes that have retired....
- St. Pontian was martyred in 236
- Benedict IX retired to the Abbey of Grottaferrata, where he repented of his sins, officially resigned as pope and spent the rest of his life doing penance.
- St. Celestine V resigned on Dec. 13, 1294, and returned to his monastery. His successor, Pope Boniface VIII, had him imprisoned so that there would be no attempt to place him on the throne again.