Closed alpha testing will begin on January 12 and sign-ups are currently open for teams. You'll need to wrangle at least four others to sign-up as teams must be between 5 and 50 players. Oh, and obviously a Facebook account is required. The sign-up can be initiated here.
Details are still slim on the game itself, but Sid offers up a few details about the overall structure of the game in his note:
Civ World games will have a well-defined beginning and end, each ending with a triumphant civilization and one person recognized as that game's most prestigious player. Along the way, as you progress through the different eras of time, you'll have the chance to win era victories as well. We want players to have both a final goal to work towards, as well as short-term objectives to achieve as they play. The trophies you unlock with your triumphs will carry over from game to game, and you can show them off in your throne room.
I'm cautiously optimistic. I'm sure there will end up being some sort of monetization scheme, but I'm hoping its not microtransactions. I wouldn't want my opponents buying gold nor would I want to spend money on a world wonder. Time will tell.