How do I apply fo a Nobel Prize in literature.

There is no application process -- you have to be nominated for a
Nobel Prize. According to the Nobel Prize web site:

"Each year the respective committees send individual invitations to
thousands of scientists, members of academies and university
professors in numerous countries, asking them to nominate candidates
for the Nobel Prizes for the coming year. Those who are competent to
submit nominations are chosen in such a way that as many countries and
universities as possible will be represented."

http://www.nobel.se/literature/nomination/index.html

The literature prize is explained by the Swedish Academy, who award
it:

"Those entitled to nominate candidates for the Prize are the members
of the Academy, members of academies and societies similar to it in
membership and aims, professors of literature and language, former
Nobel laureates in literature, and the presidents of writers’
organisations which are representative of their country’s literary
production.

Proposals for the year’s prize-winner must reach the Nobel Committee
by February 1st. A proposal should, but need not, be accompanied by
supporting reasons. It is not possible to propose oneself as a
candidate, i.e. the Nobel Prize cannot be applied for. There are
usually about 350 proposals each year.

During the spring the proposals are examined by the Nobel Committee
and in April it presents for the Academy’s approval a preliminary list
of candidates, containing some 20 names. Before the Academy’s summer
recess the list has usually been further reduced to about five names.

In October the Academy makes its choice. For the election to be valid,
a candidate must gain more than half of the votes cast. The
prize-winner receives the prize (10 million SEK in 2001) from the
hands of the King in Stockholm Concert Hall on December 10th – Nobel
Day."
http://www.svenskaakademien.se/ENG/nobelprize/

When you publish a literature, and if it's really good, then the
publishers nominate you. Then your literature will be read and argued
and debated among other papers and then the best one will win the
Nobel Prize.