How will the World Championship work in 2013? How will the World Championship challenger be determined, and then how will the actual championship match between Anand and the challenger work?  

I realize that some of the details might not yet be determined (location and specific rules).
The World Chess Championship 2013 will be a match between the World Chess Champion Viswanathan Anand, the winner of the World Chess Championship 2012, and a challenger.

The challenger to the match will be decided using an eight-player double round-robin tournament (the Candidate's Tournament), to be held in London from March 13 to March 31, 2013. The eight players will in order of rules announced by FIDE consist of:

Peter Svidler (Russia), Alexander Grischuk (Russia), Vassily Ivanchuk (Ukraine), Boris Gelfand (Israel), Magnus Carlsen (Norway), Levon Aronian (Armenia), Vladimir Kramnik (Russia), Teimour Radjabov (Azerbaijan).

The championship match is scheduled from November 6 to November 26, 2012. The match conditions (number of games played, time controls and tie breaks) have not been announced.

FIde has not determined location yet, supposedly Chennai, India is being considered, but this has not been confirmed on the FIDE website.

You can find more details here:

http://en.wikipedia.org/wiki/World_Chess_Championship_2013

http://www.fide.com/index.php?option=com_fidecalendar&amp;view=fidecalendar&amp;ny=2013