Disclaimer: I take no credit for the work done by contributors to the dreamcancel and shoryuken wikis, or any of the rest of the information in this guide. I am merely redirecting people to these websites as they provide the most comprehensive and accessible information to make learning to play this game as easy as possible.

http://dreamcancel.com/wiki/index.php?title=The_King_of_Fighters_XIII
http://wiki.shoryuken.com/The_King_of_Fighters_XIII
http://www.eventhubs.com/guides/2012/jan/26/king-fighters-13-moves-characters-combos-and-strategy-guides/

Aside from information on notation, these websites contain a huge list of combos for each character in various situations as well as move explanations and strategy tips. Pretty much everything you could want or need to know is right here.

JuiceboxAbel has also put together a great set of video guides:
http://www.youtube.com/playlist?list=PLZbBoZgd9o1neU_6e2XXm8fi7Nz0nECPL
http://www.youtube.com/playlist?list=PLZbBoZgd9o1mooAX-0W1PeIT0Q_DJ_Pta
http://www.youtube.com/playlist?list=PLZbBoZgd9o1ms5j1wwll80oTRtUTdwAnA

Frame data spreadsheet:
https://docs.google.com/spreadsheet/lv?pli=1&key=0AsrvpuirdQzwdGM0UDlRcGozMkJBQVZES0F4Zmw1MGc&f=true&noheader=true&gid=1

Mobile-compatible site with frame data:
http://www.kofxiiiframedata.com/

Community fansite with stuff:
http://www.orochinagi.com/

If anyone has anything they would like to see added to this, I'm sure there's somewhere you'll be able to leave a comment about it.