The idea here is to have a balanced team, with champions that can fill several roles, and be able to have the upper edge in 5v5 fights.
-Katarina provides solid DPS, and her Ult is spammable. She should ALWAYS take Cleanse. Buy her Damage items, and lane with Kayle.
-Kayle can build to either pack a punch or tank, and her ult will protect a champion that has to channel to be effective. Intervention on a champ that has Cleanse means pretty much nothing can stop them. Being with Katarina should at least get you an easy kill at level 6.
-Corki is an AoE god, and a great addition to any team. He lanes with Amumu. Amumu can Bandage Toss into an enemy, and Corki Valkyries in to shut off any chance of escaping. This allows for sudden kills, and Rally will give the extra advantage needed to push and hit hard.
-Twisted Fate gives the team map control, global slows and AoE stuns. He's the one who should solo most of the time, as he is great at farming and ganking. Exhaust is there to make sure the enemy can't escape, and Ignite helps deal the killing blow for early kills.
-Amumu is the team's main tank, and should usually stack Sunfire Capes. Another champion that should take Cleanse, and a secondary target for Kayle's ult.
The Summoner Spells not listed in this description are suggested, but not mandatory.