Ok before you start on your jungling journey, i want to tell you to only teleport back to spawn when it's absolutely necessary. such situations would be:
-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:
-Blue Buff Golem ~ Smite + Get a teammate to hit the Golem then run away to reduce damage to you. they can even stay to help do damage as long as they do not take the buff.
-Wolves
-Wraiths
-Golems
-Enemy Wolves ~ then "B" and buy(Madreds Razors)
-Red Buff Lizard ~ Smite
-Wolves
-Wraiths
-Golems
-Enemy Blue Buff Golem ~ Smite
-Gank Bottom or "B" To Get(Berserker Grieves) ~ if you do not have enough money to buy berserker grieves, then go (Wolves, Wraiths, Golems)
-Kill Dragon ~ Smite + I suggest that if you don't kill the dragon with a teammate, then you should start building the Hextech Gunblade and buy a(Vampiric Scepter) so that you can life steal the dragon.
-Now you can continue jungling with either this same route over and over, or you can start ganking and helping out in lanes and only jungling when the buffs are available.

____________________________________________________________________________________________

If you do not have a teammate that will help you out with mana buff, take this route:

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. but only teleport back to spawn when it's absolutely necessary.

Items Needed at Game Start
-Cloth Armour
-2 Health Potions
-2 Mana Restore Potions

-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, that 15% chance can allow you to get the buffs incredibly easy, as well as finishing your route in very little time.
_____________________________________________________________________________________________
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 life steal, 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.

OR

You can replace the frozen mallet with a Deathcap which will give you 120 ability power. the reason for this would be to add more damage to Hungering Strike which will benefit you very much if you can pop it off after a successful Infinite Duress, which will allow you to get them to half health and let Blood Scent kick in so you can chase them down for the kill.

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 (or around 450 with Deathcap) damage or so when you enter end game, and your melee is 300+ which is amazing.
-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.
-When playing higher ranked opponents, they usually see your smite in the loading screen and they will try to kill you off the start when your at mana buff. so you will need the lane that you a next to to watch the river, or you can even ask mid to watch your back to.

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 i do care about your opinion, and i do want feed back on my guide as i want to improve and become better. so please leave a vote and a comment telling me what you thought about my guide. Alright, I'm Out.

- DAT ftwbotter :D