Nunu is a good pick if the enemy team has low mobility to escape your ganks. He synergizes well with ranged attack damage champions with his blood boil (w ability) which grants attack speed and movement speed. He also synergizes with tanky damage per second champions such as xin zhao who lack a bit of attack speed if they buy warmogs and the atmas impaler.

Don't get the idea that counter jungler is always good because it is not. If the enemy team has a strong jungler who ganks well, than nunu is the choice. If the jungler is considered average, than a counter jungler is not necessary. Make sure that the bot lane is able to sustain against a 1 v 2 or even if you do succeed in countering the enemy jungler, the bot lane will miss many creep kills and the tower will die. If the tower dies at bottom, the champions in the bot lane may gank other lanes as well.

The point of counter jungling is to deny the jungler in experience and creep kills. Those who rely on wriggles latern and get counter jungled wont gank as effectively. Make sure when you counter jungle to always place the ward you start off with at either the blue or red buff depending on the enemy jungler. If the champion is a mana champion, it is best to place the ward at the red buff. Once the minions spawn, take the big wraith with consume but if it is guarded take one of the double golems with smite and consume. Then if the enemy jungler hasn't reached wraiths just go consume it.

Always snowball the enemy ranged or dps carry because it decreases their attack speed a movement. Once the ranged carry is slowed with the iceball, your teammates should attack them. Remember to always keep an eye on your blood boil and use it when it is off cooldown.

When you're focusing an enemy ad carry, they tend to attack you. A lot of high elo players who play ranged ad hit those bursters who chase them. The banshees is just to stop one cc attack so you can further chase the ad carry and speed up your ranged ad. If your ranged ad is vulnerable, protect the ranged ad with your snowball. If your ranged ad has high mobility then SPAM AWAY.