Warwick is a really powerful jungle champion because of his bag of trix. Hungering strike doesn't heal you as much as it once did, but both that and Hunters Call will help your team and give you a very quick jungle. Warwick is also a very good ganker once he reaches level six, as he can quickly undo an enemys attempt to escape.

I usually start out at the two Golems, using smite to kill the big one. Then i transition to the wraith with no trouble, then i ask the middle to pull the Ancient Golem, grab that with smite and then easily take out the Lizard Elder. I repeat this until i get to level six, when i look for a gank. Always make yourself able to gank. Also, dont go b before you have about 700 gold, so you can buy the Emblem of Valour and some boots. Repeat the jungle until you are needed in lanes and teamfights.

Your role in a fight is to wait until their highest burst character present themself, then you tag them with your ultimate and ask your team to collapse on them. Then you try to take on squishies first, allowing you to easily following them with Ghost and Blood Scent. If you and your team do well, you will easily clean out their team. Remember! It's only fun if they run!