Ok before you start on your jungling journey, i want to tell you that you shouldn't hesitate to use your potions. This also means though, that you will need to teleport back to spawn to buy some more potions to stay alive. only teleport back to spawn when it's absolutely necessary though. such situations would be:
-Out of Mana / Mana potions. ~this should only be an excuse when you know you can't kill the mana golem.
-Low HP with no health potions ~ that is obvious but some people might not know.
-When buying Madreds Razors / Berserker Grieves

My route to take when jungling is:
-Golems ~ Smite
-Wolves
-Wraiths ~ Smite the blue wraith
-Golmes ~ you should only have to use Hunters Call & Hunger Bite to take these guys down.
-Wolves
-Wraiths ~ then i usually have enough to buy my Madreds Razors.
-Mana Golem ~ if you are a bit scared of this, do another cycle of (Golem, Wolves, Wraiths)
-Red Lizard ~ you can probably do one more cycle of (Golem, Wolves, Wraiths) and then teleport back to spawn and have enough for berserker grieves.
-Dragon ~ this is all that is needed and then you can start ganking as you will be level 6. if you are not, then do another cycle or go steal the other sides mana buff or red buff.

Alright before i talk about the final build items, i just want to say that Madreds Razors are a junglers best friend. they give a 15% chance of doing 500 magic damage to all minions and creeps. depending on your luck, you can get the buffs very easily.
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The Infinity Edge can be replaced with a Blood Thirster but the damage is lowered, and the critical hit maximum damage. plus there is no need for any more life steal. And when your playing as a DPS Melee, you want a much damage as possible.

Madred's Bloodrazor is Warwicks weapon. it's basically a tank killer. in my opinion, the bloodrazor is a must. and it's attack damage boost is always good to have :D

Some people say you don't need a phantom dancer as warwick. hell, 55% attack speed and 30% critical hit chance improvements aren't worth it? plus some bonus movement speed? yeah, my ***.

The Hextech Gunblade is an item i don't see many warwick players use. i think it is a perfect item for him, with lifesteal, attack damage, and some ability power. plus its passive can do 300 damage which is pretty good mid game if your looking to do massive damage in one short burst.

Berserker Greaves can be replaced with something like Boots of Swiftness or Mercury's Treads, but i think the greaves are the best choice because of the attack speed bonus they give which is essential to have early game.

The Frozen Mallet is really just an item i use because late game when you actually have enough money to finish this build, it's pretty obvious you could use some more hp. and slowing enemies is very helpful too. getting more fed never hurt anybody.

Smite is an obvious selection because well, your jungling. and being able to do true 450+ damage to minions / creeps at all times is essential. nuff said.

Flash can be replaced with ghost if you are not rank 12. Though if you are above rank 12, i strongly recommend Flash, because you can jump to the other sides of walls, you can get away much easier than with ghost in my opinion, and sometimes it will get you just the distance you need to be to pop off an Infinite Duress so you can get them to half hp and blood scent them so u can run after them with a Hungering Strike or some normal melee hits to get a kill.

When jungling as warwick, you should always know when to help your team mates. this is much easier when playing with people you know. if your all alone in a 5v5 with randoms, start up a conversation, get everyone talking and make sure your team is calling MIA's, because that can lead to a fed Twitch or Tryndamere, and nobody wants to be in that kind of situation now do they?

Anyway, as a jungler, you are running all over the map, and there are going to be many opprotunites to gank, but you need to remember, just because you have the buffs and are full mana and health, you can easily be killed by 2 people even if they are half health. so make sure your teammate knows that you are going to gank and who you are going to target.

Pros:
-Massive damage, Hunger bite is doing about 350 damage or so at the end.
-Can clean up kills
-Can 1v1 almost any Enemy
-Gets ahead early game.
-when some enemies click the map to go to a place then click away to watch a fight, you can pick them off when they aren't paying attention walking through the forest.

Cons:
-Can get killed in the jungle randomly by enemies passing through
-Usually initiates team fights which make him the first target for 5 others.
-Can't really do damage to enemies like Xin Zhao or Tryndamere until he gets infinity edge or is with a teammate.

All in all, I would say that warwick is one of the best DPS Jungling champions out there. the only person that i think is better than him at jungling is Nunu because of one of his abilities that lets him do massive damage to minions / creeps + smite. but i think warwick is the better champion. plus who doesn't love listening to warwick talk? "It's only fun if they run". That is the most awesome thing i have heard a champion say so far.

Anyway, good luck in the jungles, and if you have anything to add to any comments, leave then in a comment below. and remember to vote as well :D