Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Early game -
MF starts off mid allowing her to reach lvl 6 quick. Amumu starts off jungling leaving Anivia to turret hump / solo 2v1 until lvl 6. Kennen & Galio lane together which allows Kennen to benefit from Galio's abilities. Played right Ken and Galio can slow / stun their way to an early kill or two and the first turret down. Also, if Ken and Galio take bot lane they can quickly move up and kill the dragon.
Mid game -
At this point MF and Anivia should both be lvl 10, Amumu, Ken & Galio should be lvl 8 or 9 - granted this all depends on the KDR. Regardless, this team make up should destroy in any team fight ... IMO. This is the theroy behind my madness:
Amumu leads the way with Galio right on his heels. Once the other team gets into "mage" range, Galio uses Righteous Gust allowing Amumu to increase his speed and ultimately use Bandage Grip and his ult. Galio followes in using his ult to taunt those in range - Ken lightning rushes in behind Galio and uses his ult on the way in then surge. This should now stun 3 - 4 champions allowing Anivia to get in good position to ult (typically right in front of Amumu / Galio). MF should be near or in front of Anivia to ult which in turn should protect Ken, Anivia and MF from anyone wanting to focus them down. Between Galio, Ken, Anivia and MF's ult's ... no one should be alive unless they run.
You could swap out Nunu for MF, however the reason behind MF in this team make up is for the MR most teams will most likely stack to protect against the heavy magic dmg that will be put out.
*I look forward to any and all comments on this team make up / build.