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.
Concept team, more or less designed to destroy team fights and have a really aggressive early game.
Kennan will go mid, Kat will go top to solo, while Nunu and Yi will go bottom and be the most aggressive lane.
Udyr will do what Udyr does best and jungle/gank like a boss. If you need instructions on how to do this, look at other builds. This topic has been covered extensively and more thoroughly then I am able to do so, so you may as well get your information for that elsewhere.
Most Nunu players that look at Nunu's build will dismiss it because it is very much not a traditional Nunu build out...which is sort of the point. Nunu makes a simply amazing lane partner for Yi, and the boil blood will allow both of you to simply plow through the enemy force and take out the tower FAST. Yi can farm like a champ with just one level in his Alpha Strike. You've got enough CC between Nunu's slow and Yi's exaust that most champions simply can't get out of there fast enough. Add to that the run speed and attack speed from Nunu and Yi will be ripping through just about anyone they send down there. Once that tower is down, go do it again in another lane. Rinse/repeat. You should have two, maybe even all 3 towers down by the 12 min mark.
Kat and Kennan are pretty standard. They both solo exceptionally well, and again it's really a topic I don't need to cover here. If you need instructions, go look them up. They are easy to find.
This is important, so it gets it's own chapter. STAY WITH YI AT ALL TIMES. I cannot stress this enough, you will get plenty of gold if you just stay with Yi.
Roaming/Team Fight Phase
So, here is where the magic happens. Udyr/Nunu will initiate (thus the banshee's veils) and Kennan will follow in right behind them, with Kat bringing down the hammer. Yi will then come in and clean up anyone who managed to escape.
Udyr will stun the carry, Nunu will begin his ult, slowing their entire team. At the same time, Kennan will run in and use his Ult/Lightning Rush/Electrical Surge combo to stun and further slow the other team. This gives Kat PLENTY of time to jump into an ideal position for her Ult to clean up handily. Yi should be able to kill any stragglers by this point (as even if they flashed out they probably got hit with at least some CC) and grab the ace with Nunu's fine assistence.
Now your whole team is on cooldowns, so Udyr, Yi, and Nunu will go beat on the tower and take it down. Kennan and Kat will auto-attack it but their damage will be minimal by comparison.
Rinse/Repeat to victory.
Pick a 'commander' for the team. This is the person who will coordinate the team fights and count down. Know what number of the count you need to run in on.
The best positions for this commander is going to be Udyr or Nunu since they are initiating. Others CAN do it but it will take practice.