Warwick is a champion normally used as off tank, or even dps. I will show you a detailed guide of how to use warwick with ability power. He only has 1 spell that benefits from ability power but it's almost spammable, you are near tank and do loads of damage, trust me.
Please read EVERYTHING and try it out in games before voting or commenting, Opinions are greatly appreciated.
The first 6 items are ussually what I go for, after those are the other choices or what you could need in some games.
All I have to say is :use it, love it, spam it, heal with it, kill with it, tank with it.

Pros:

-Can tank
-Can nuke
-Can get himself to full hp in a matter of seconds
-Can tower dive
-Always dominates his lane.

Cons:

-Can be countered with CC/Quicksilver headsash
-a bit squishy early game
-Very low mana pool

Eternal thirst:Your passive: The more you attack someone, the more you will heal from it with your auto attacks.
Hungering strike: Your bread and butter skill, it deals damage and heals you.
Hunter's call: It increases your attack speed and the attack speed of your allies by half of what it increases yours.
Blood Scent:Whenever someone is at below 50% hp and in range of this spell, you have vision on him and your movement speed is increased.
Infinite duressYou jump on someone, suppressing, dealing damage and gaining more lifesteal, make sure you don't use it on people like Gangplank who can use their W to evade it, or people who have quicksilver headsash.

I go formagic pen quint/marks because people who stack magic resistance are going to be annoying, and you're mostly a mid/end game champion when going ap. You can either gomana regen per level orhealth per level seals, if you find yourself mana starved a lot, go for mana regen per level, if not go for hp per level as you are a bit squishy early game without your ap. I go forap per level glyphs to start having a good amount of ap starting mid game.

Utility and offense is the best choice as it gives you the early game lane dominance, cooldown reduction, and reduce cooldown of summoner spells which is essential to have your flash more often to kill or escape. The offense for penetration of magic resistance because I assure you that people who stack magic resistance are extremely annoying late game, you want the magic pen.9/0/21

Start with afor the mana regen and hp mostly. Afterwards, getbecause you are quite slow. Then I go for, ask why? Let me tell you. It gives ap - It removes magic resistance which works with my ult as it is on hit and gives us attack speed. Why attack speed? It helps you last hit, it helps you have another way to heal yourself because of your passive, and most importantly helps you have another way of dpsing when your Q is on cooldown. Then go for afor the as and ap and the cd reduction, spammable Qs and ults on 40 second cooldown ftw?for the spell vamp/ap , you will heal yourself to full almost instantly at this point. At this point of the game it's up to you to see what you want. Do you need more burst? Get, your Ult plus DFG plus Q = dead. You need survivability?or, Banshee for the heavy ap nukers, you'll be able to nuke them faster, Guardian angel to revive in a team fight not with 700 hp, FULL hp because all you have to do is Q. Need more healing/dpsis a great choice as well, it increases your dfg's dmg, your healing with Q and your Q's damage. Too much magic resist on enemies?! Need even more burst?. Want more damage on your auto attacks?!
And finally, getting cced too much? threads or moonfire spellblade.

I max out the Q of course as it is your main spell, W next to heal with your passive and the attack speed from items, E last because if you're chasing, the enemy must be very close to you so no need a big range. Of course take R whenever it's available.

First of all I hardly advise you duo lane, because a combination of your ult, your Q (used to tower dive if needed) and your allie's help, the ennemie is pretty much dead.
Before you get your ult I advise farming a lot, Q the enemie if he gets too close, and if you get harrassed use your Q to last hit a minion and heal yourself as well. Starting level 6, you can now devastate your opponents, Tell your allie that you're going in, use your ult, your Q and ignite, follow if needed because you can tower dive if you can reach your Q to a mob or eve the ennemie. Higher level, use DFG/hexteck gunblade if you have them and you will have a huge nuke.

I takeflash andingite, Flash for the ganks or when I need to escape, ex: Flash in ult, Flash out of Jarvan ult.
Ignite because I tend to chase a lot and you don't want supports to heal up someone you're about to kill.

Have theblue buff WHENEVER it's up. You just need it, harassing your enemie with your Q will surely result in either a kill or you denying him because he recalls. Early/mid game, since your carries are farming I also advise you grab red because I personally tend to chase a lot. Late game, keep it for your carries though.
End game, I recommend you sell your Doran's Ring and Malady and exchange them with something you need.

When in ranked games, you really need to play extremely safe, you never know when the jungler is coming to gank you because you're farming too much or something. BUYWARDS, Ward whatever you can don't trust your allies or the support, ward dragon the bushes near you, baron, trust me. When in teamfights, you want to agree with your team mates who to focus first, your job is to ult him and nuke with your Q chase if you're sure you can kill him, if he flashed forget him and continue to Q and auto attack the others. End game you can pretty much tower dive and survive most of the times just make sure there are creeps nearby so when the ennemie is dead, you can still heal with your Q on them.

You don't jungle with ap wick, but the jungle helps you a lot. Blue buff is extrmeley necessary. Whenever you're low hp and feel like you're gonna get tower dived, go to the jungle Q a creep at max range so he doesn't hit you and go back to your lane. You can solo Baron and dragon end game but don't do it without your team as you're extrmeley slow at doing it ;p.
In lane, before recalling push the creeps and take some creeps of the jungle to make sure you get the most gold.

Always talk to your team, make sure they know who to focus, who you're going to ulti, how to counter some champions like annie for example, make sure your team spreads out or you're instantly dead.

Farming is extremely important with Warwick, you need gold. Normally you will get a lot of kills early game, but if your opponents are tower hugging or playing very defensive, make sure you farm but WITHOUT pushing only last hit, you don't want to get ganked.