First line: Email
support@neogaf.com
Second line: Contact a moderator on Steam, Twiter, XBL, PSN, etc.
Comments will be read, but you won't necessarily get a reply. It's not necessarily ideal.
Note: If the appeal consists of any of the following, it will be totally ignored:
a) "The rules are bad so they shouldn't apply to me"
b) "Someone I don't like did something like what you banned me for and they didn't get banned so I shouldn't be banned"
c) "Mods are biased"
d) "I know I got banned for a two word post telling another member to fuck off, but here's a multi-paragraph clear explanation of the point I actually wanted to make and as you can see my point makes sense so why did you ban me?"
e) "I think my ban should be shorter because in my head bans should be shorter"
f) "Explain my ban only use more words than you did in the ban message"
g) "I demand to know which mod banned me and when they will be resigning"
I just mention this because these are like 95% of the appeals we get and it's really not the kind of behaviour you'd expect from, like, adults in the real world.