Okay, great. Now you need someone to manage this page. I can't, I'm already editor in chief of polish Urban Terror Portal. But I can share some thoughts. Person responsible for FB will be called by me "FB guy".
Whenever someone commits something new, which can be "screenshotized".
Mapper commits new map. It's his duty to load UFO in ULTRA HIGH OMG settings, make some screenshots and send it to FB Guy. FB Guy makes a post on FB. He puts a pic and short comment. SHORT! Don't write essay about new feature. Use one long, or two short sentences.
Example:
Our mapper's team is proud to present new Alien Base map!
OR
After many weeks of work, meet our new armor for Marines:
<another pic>
If you are lucky, and in one day you have more than one material, that can be posted on FB, don't be greedy. Wait 2, 3 days and post it. It's important, that updates are constant. So you must work like TV Newsroom - calculate your material's time "on air"
You can as you players for some funny screenshots, like mine for example:
That's why you can equip your soldiers with grenades :-)
And so on. Make sure, that "something happens" constantly. You are not going to get popularity like Gaga on the start, for a long time you will be almost without fans. You need to endure this early phase
DESIGN
Dear God, I don't know who is your lead artist, but get the guy/girl and make him/her to make some nice pic for page.
Moreover, you can think about narration of your game. Maybe you can start talking about this game, like we would having REAL WAR with aliens now? Something like Wells did
http://en.wikipedia.org/wiki/The_War_of_the_Worlds_%28radio_drama%29Dunno, something to give UFO:AI "soul".
And last but not least, button of FB should be bigger imo on your start webpage.