The difference between a normal Organized Play character and an Organized Play Core Mode character is very simple: Core characters can only use certain options, most notably the Core Rulebook. Core characters can also use the Character Traits Web Enhancement and the Roleplaying Guild Guide. No other products (Pathfinder Player Companion, Pathfinder Campaign Setting, Pathfinder RPG - Ultimate... or Advanced... books, etc.) can be used as legal options for a Core Mode Character.
The Roleplaying Guild Guide details every thing you need to know about making Pathfinder Society characters, in standard or Core mode - it's the newest version of the book formerly known as the Guide to Organized Play, and is the rules for PFS.