You must be either a part of the media, store that sells video games or a developer.
There are free tickets but you need to jump through several hoops to get them.
You don't need to be invited but there is a lot of really annoying verifications you need to do. (Check stub to prove you are from the said company, and the like. I started my own company but never did go anywhere with it because of various issues, but I was able to go E3 several times.
e3expo.com
Go there hit register, attendee and there is a FAQ that covers everything. (The FAQ is within an applet so usually posting the direct link will not work.)