Skills
Eternal Thirst - Each of Warwick's attacks will heal him for 5/10/15 health. Each successive attack against the same target will restore increasing amounts of health to Warwick.

This is a skill that allows Warwick to jungle from lvl 1 very efficiently.
Simple, you hit a target = you get health, even without lifeseal.

Hungering Strike - Takes a bite out of enemy unit for damage and heals Warwick.
Strikes an enemy for the greater value between 75/125/175/225/275 (+1) and 8/11/14/17/20% of the target's maximum health (can only do flat damage to monsters), and heals Warwick for 100% of the damage dealt.

Cooldown - 12 seconds
Cost - 100/100/100/100/100 Mana
Range - 400

Take note this is a 400 range skill. It's great for keeping yourself alive, while facing other team carry champ. You maybe have lower damage, lower or 0 lifesteal that time, but with this... he will be down before you are, and he will probably start to run away... worst thing you can do while facing warwick XD. You should use it right after ultimate and to finish off that last fiew points of health.
After maxing out that skill you can use it to get health back after a team fight in the jungle and get back to fight without beeing forced to go to base.

Hunters Call - Warwick lets out a howl, increasing all nearby friendly champions' attack speed for a short time.
Warwick lets out a howl that inspires all nearby allied champions. This increases Warwick's attack speed by 40/50/60/70/80% and all nearby friendly champions' attack speed by half of that for 10 seconds.

Cooldown - 30/27/24/21/18 seconds
Cost - 35/35/35/35/35 Mana
Range - SELF

No longer a global skill. Now you have to make sure your teammate is in range of getting it :( The duration is AGAIN a fixed time and the change is only in AS bonus. Still you wont have to max out this skill early or even mid game anyway :P
Proper usage is Ulti->Hungering->Hunters Call.
Get 1 point of this skill as your 1st choice and start jungling. Use it on CD, since it has nearly none mana cost
This is the skill that allows you to focus on important items instead of stacking atack speed ones before going core.
If you see a warwick with malady... you can laugh in his face and eat him :)

Blood Scent - Warwick passively senses weakened enemy champions around him. The scent of blood sends him into a fury causing him to move at incredible speeds.
Warwick senses enemy champions under 50% life within 1500/2300/3100/3900/4700 distance of him; Upon sensing an enemy at low life he will gain 20/25/30/35/40% Movement Speed.

Cooldown - 45 seconds
Cost - Passive
Range - SELF

Blood Scent is a best ingame skill for catching fleeing enemy champs, as well as running away from a loosing battle (if one of their champs have <50% hp).
This should ALWAYS be picked at lvl 4 and maxed out together with Hungering strike and ulti.
You should be able to get som1 to <50% with your Ulti+HS combo, witch enables Blood Scent and just run and kill. So you can call it a passive movement speed increase :P.
It also reveals any enemy player that you have scented on map even in bushes.
It will enable itself if you have a <50% stealter near you as well. But you will not be able to see them anyway.

Infinite Duress - Warwick lunges at an enemy Champion, stunning them and dealing damage for a few seconds.
Warwick lunges at an enemy Champion, stunning them for 1.7 seconds. While they are stunned, Warwick quickly strikes the target 5 times for 33% of his attack damage plus 40/60/80. Warwick gains an additional 30% lifesteal while performing Infinite Duress.

Cooldown - 90/80/70 seconds
Cost - 100/125/150 Mana
Range - 700

This is your cookiecutter skill.
It got rebalanced last patch making it less mana eating, better damage, and lower cd. The stun duration nerf is not that important (2.1s -> 1.7s)
They also added a lifesteal addition. This makes tactic 1v1 and 1v2 a diferent story. If you engage an enemy and you are quite sure he/she will fight back, not run away, try using Infinite Duress a bit later.
The usual fight against enemy carry is:
HC+Melee them with spamming HS on cd. When i see him/her going down quite at the same rate (or when i feel i am loosing i use ID moment i reach 50% HP. The new lifestealing will heal me quite a bunch, usualy making enemy try to retreat. And as Warwick says... "It's only fun if they run". Its the worst they can do.
This tactic also can be implemented in double lane solo v 2 fight. Usualy you are ahead of lvl and they are weakened after a fight 2v2. Your teammate dies and you are left with 2 nasty champions that try to hurt you.
You SAVE your ultimate. Kill one, and when 2nd one tries to escape you catch him with ID or when you are realy low on HP, you do it on 2nd one to heal yourself up.
Remember, lifesteal bonus is quite a nice bonus to your ulti. Dont rush it if you see the option to get to them just by running of flashing. Hit fiew times, and than finish off with ID+HS.
You have to take into consideration that you will simply hit 6 times your atack. So all "on hit" items are getting stacked extremaly fast and in very efficient way.
That means you will get 6x4% from Bloodrazor, you will get 6x42mana=42damage from writs end, 5 stacks of Black cleaver debuff just in 1 ultimate atack. Sick!
with all that damage it will calculate in more or less this:
200Atack = 66 per atack
6x66 damage = 396
6x4% max health (example 2000 Health) = 6*80 = 480
6x42 mana = damage = 252
Total 1128 damage.
Target is debuffed with 5 stacks of black cleaver so bye bye armor, and he will be below 50% for sure if not, than 1 HS will do the job. Just execute than.
(i know there are magic resistances and armor **** bla bla bla, this was just an example).
Lvl up this skill on lvl 6/11/16 always when it's avaible.
Get golem neutral buff to lower down it's cd all the way. Gank whenever it's up. Catch players near tower with it to maximize the damage they recieve.
Think of clever usage of blink+ulti from the jungle.


Items

You should focus on getting your Ultimate as powerfull as you can.
This is why your item build should look like this: