You have to request and to be eligible you must have been a EC member for at least 2 weeks and have had to have made at least 50 posts.
You have to be a member for 2 weeks and make 50 posts. Then you can follow this link here and fill out the application.
I'd like to ask something to clarify: do the posts have to be made in places other than the Fun and Games section? I'd thought there was a somewhat recent rule that said as such. Or was that removed?
As I recall, Fun & Games no longer counts for the Full Member upgrade. But this was supposed to be taken care of automatically--the post count under your name was said to no longer reflect any Fun & Games posts. That is, you post 1 billion posts in Fun and Games, and 1 post elsewhere, and your total post count under your name will be a whopping 1.
That is correct. It doesn't work retrospectively though, which is why nobody's post count decreased when the change was made. The general policy on posting is to post across various forums, rather than just in one section. However, that aspect of posting probably isn't as vital now that Fun and Games is not factored into post counts. It certainly doesn't hurt for applicants to post across various forums, but its more important to have posts that have substance to them. It wouldn't be, for example, feasible to get an accurate picture of a member's activity and suitability for full membership if they just had 50+ posts of "welcome " in the Welcome Lounge forum, so in that regard the need to post across various forums is still there.