He is elected by the College of Cardinals, by secret written ballot, at the Vatican. To be elected Pope a cardinal must have two thirds majority + 1 of the votes.

NOTE - under new rules brought in by Pope John Paul II
" if a certain number of ballots have taken place without any Cardinal being elected Pope, then the Cardinals may then elect by simple majority" (1)

The voting process and ballot process is long and complex and new changes will certainly make it easier for a new Pope to be elected. The voting is secret and helps promote a fair election ( 2 )

Both sources go into detail outlining the process of election as well as the death of a Pope and the calling of the Cardinals for the election.

There are 120 elector cardinals who are going to elect for a pope. This is the primary role of the cardinals although they have also responsibilities within their area of jurisdiction.These cardinals must be under 80 years of age, of sound mind, and present in person at the elections to be eligible to vote.

A Pope is elected by Sacred College of Cardinals called the conclave, by ballot. Balloting continues until the vote reaches two-thirds majority.

-quote-

"Popes will be elected by full vote of the Sacred College of Cardinals by ballot.

The election of the pope almost always takes place in the Sistine Chapel, in a sequestered meeting called a "conclave" (so called because the cardinal electors are theoretically locked in, c*m clave, until they elect a new pope). Three cardinals are chosen by lot to collect the votes of absent cardinal electors (by reason of illness), three are chosen by lot to count the votes, and three are chosen by lot to review the count of the votes. The ballots are distributed and each cardinal elector writes the name of his choice on it and pledges aloud that he is voting for "one whom under God I think ought to be elected" before folding and depositing his vote on a plate atop a large chalice placed on the altar (in the 2005 conclave, a special urn was used for this purpose instead of a chalice and plate). The plate is then used to drop the ballot into the chalice, making it difficult for any elector to insert multiple ballots. Before being read, the number of ballots are counted while still folded; if the total number of ballots does not match the number of electors, the ballots are burned unopened and a new vote is held. Otherwise, each ballot is read aloud by the presiding Cardinal, who pierces the ballot with a needle and thread, stringing all the ballots together and tying the ends of the thread to ensure accuracy and honesty. Balloting continues until a Pope is elected by a two-thirds majority."

-end of quote-