There are no clan challenges in Ghosts. I know for some items you need you and a clan member in the lobby to earn XP but not sure if that applies in all game modes or not. It would be wise to have at least 2 people that can play around the same time.
The way I read this from the /ghostclan section of the web page is "
Call of Duty®
Battle for territory against multiple Clans of similar skill. Earn exclusive Call of Duty® Clan Wars items and XP Bonuses by dominating your opponents."
So that tells me you're entire clan (2 or more??) will be able to compete as a clan against other clans.
Check this link out for more information on clan games --> Call of Duty®: Ghosts
Here's some items from the Early Registration FAQ: http://community.callofduty.com/thread/200777474#.UmloVChDsjI
Q: How do I level-up my Call of Duty®: Ghosts Clan?
A: In Call of Duty®: Ghosts, all multiplayer matches played with at least one other Clan Member will earn Clan XP and unlock Clan rewards.
Q: What is Call of Duty® Clan Wars?
A: Call of Duty® Clan Wars is a brand new game mode in the Call of Duty® app that ties directly to Call of Duty®: Ghosts multiplayer. It offers a deeper Clans experience by enlisting players into a larger conflict where any Clan Member, regardless of skill level, can contribute to the Call of Duty® Clan War simply by participating, and rewards them with cool items, both in the app and in Call of Duty®: Ghosts multiplayer.
My guess as to how this will work is as follows:
Playing Solo - Every Win will contribute a point to your Clan Wars Objective and potentially move you closer to bonus XP. Winning the match does not earn your Clan XP or unlock clan rewards.
Playing with 1 or more clan members - Every win will contribute 1 point per member to your Clan Wars Objective and move you closer to bonus XP from the Clan War. Winning the match will also earn your Clan XP and unlock clan rewards.
Maybe I'm reading into this or reading it wrong, but that is my understanding of how it will work. Either way, it is probably best to play alongside at least one other fellow clan member.