Next update will be on items and masteries

(I'm still working on this, got a few more chapters to add, just don't have the time to add them currently, I released it as it is to get some feedback on how to improve it. I also have quit a bit of coding to enter to get the right format and all the images and links.)
This is my first MOBAfire build, and I thought I'd go with a champ I have had a good amount of luck with in the past.
Most people prefer to jungle with warwick but there are a lot of junglewick builds on MOBAfire already so making one of those would be pointless.
Ok, so the way I play lanewick is that I start with AP, slowly transitioning to attack speed and on hit effect items. The starting AP makes him a great harasser and gives him insane sustain, the attack speed and on hit effect items work with you ult and your W to put out all sorts of debuffs and damage.

Marks: Greater Mark of Scaling Attack Damage, I get these because of the good attack damage scaling, these overtake Greater Mark of Attack Damage at level 7, which is when you'll start making more use of your basic attacks for killing enemy champions.
Seals: Greater Seal of Attack Speed, the reasoning behind getting these is that warwick's passive ( Eternal Thirst) is that he gains life with each hit, as this is a set amount, the extra attack speed helps get lifesteal from minions faster, it also makes it quicker to kill enemy champions.
Glyphs: Greater Glyph of Ability Power. These are to make your Hungering Strike a more effective harasser as well as giving you more health when using it. This gives you more sustain and better harassment.
Quintessences: Greater Quintessence of Ability Power. I take these for the same reason as the glyphs, better sustain and harassment.

Ok for masteries it's 21 0 9 (shown above) making sure to get all the AD style offensive ones (except for offensive mastery) and one in archmage's savvy, burning embers and 2 in sorcery.
In utility you want all 4 xp bonuses, the neutral buff duration and 3 in mana and health regen and 1 in good hands (in case you do actually die).

• You want to get Hungering Strike at level one to open straight up with some harassment.
• You want to get Hunters Call at level 2, this is incase you have a beast of a lane partner and you two have already sent the enemy packing to their turret to turret hug.
• Then at level 3, you want Blood Scent, for obvious reasons.
• Max your Hungering Strike first, as you will be using it as your main source of damage until the laning phase ends.
• Then max your Hunters Call for all the extra attack speed.
• Finish by maxing your Blood Scent.
• Level your ult, Infinite Duress, at the normal intervals (level 6, 11, 16)

Ignite: When killing an enemy you're going to be close to them, so if they're almost dead but about to run past their turret then this can get you a kill that you wouldn't have gotten otherwise. With the enhancement it also gives attack damage and ability power when on cooldown.
Flash: Even with it's nerf, which makes it more difficult to flash over walls, this is still my favourite summoner spell. It can get you out of many bad situations, and if used correctly can get you completely away from danger. It's enhanced version has a lower cooldown.
Exhaust: When you're chasing you will most likely have brought their health below half, so you will be faster, but this can be used when they're near turrets to stop them getting into their turret's range or out of your turret's range. It is also good if you have someone chasing you, as it takes away a good bit of their damage and speed, and 9 times out of 10 making them give up on the chase. It enhancement reduces the opponents armor and magic resist.
Ghost: If your opponents are not at half health and someone is ganking you then this can help you get away and is a more viable choice because of the recent nerf to flash. It's enhancement improves its movement speed bonus.
Teleport: Seeing as you do not have the xp boost mastery any more, the ability to return to lane instantly after needing to go back will help you keep up with, or extend your advantage of, xp gained. It's enhancement reduces it's cast time.
Promote: Promoting a minions early when you engage the enemy or they engage you, will be invaluable as the promoted minions do a very good amount of damage, making it so that you have a much greater damage output than the enemy, this could be the difference between you dieing or getting a double kill. It can also be used late game to cause a sneaky minion push while your team is (hopefully) steam rolling mid. It's enhancement improves the defences of the promoted minion.
Heal: If you're in a situation where you would need an instant heal, I don't think that the little health that this will give will save you. It's enhancement improves the amount of health restored.
Revive: I would much rather take a spell that would save my life than one that revived me instantly, as this would make me able to circle around and ult into the fight again, and it also wouldn't give them the gold for killing me. It's enhancement grants a speed buff when used.
Smite: You're not jungling using this build so smite isn't going to help much. It's enhancement gives you 10 gold on each use of smite.
Cleanse: Clearing yourself of cc is probably not going to help, as they will most likely have more than one stun/snare so you will just be stunned or snared again. It can be replaced by Moonflair Spellblade, which gives tenacity and some ap. It's enhancement Increases the duration that you are less affect by cc for.
Clarity: You may be mana hungry, but this will only be useful early game, as late game you will not be mana hungry at all. Blue buff can also massively increase your mana regen as well as decrease your cooldowns, making it a much better alternative. It's enhancement increases the mana restored.
Clairvoyance: This is a skill that should be used by the support, as it supports do not go diving in to kill people, which is what Warwick does, so he needs the escapes due to his e ending when he kills the enemies.

First item is a doran's ring, very nice item as it gives health, mana regen and a nice bit of starting AP.
Next up is kage's lucky pick, this gives a good boost to your ap, and the 5 gold per 10 makes it quicker getting your next items.
Your third item is malady, you'll be getting this roughly the same time as you start using your ult more often, so the magic resist shred, combined with the 20 magic damage per basic attack and your W and Q make this ideal for getting early kills.
Next up is wit's end, this item works well with warwick because of it's passive, it will be activating the same time as malady's passive, giving you more magic resist, making you more resistant to those nukes which would normally destroy you.
Ok, next up is the classic WW item, madred's bloodrazor, this is insanely good on ww because of it's passive and attack speed, as well as giving some damage and armor. You should build this in the order: recurve bow -> pickaxe -> madred's razors -> madred's bloodrazors. The reason this works so well it that malady's magic resist shred combined with this makes warwick's ult do more damage each slash, it is also a great counter to health tanks such as vladimir.
Next item is sunfire cape, this is good because it deals magic damage to nearby enemies, so while your ulting someone, they're taking even more damage per second because of the cape, as well as malady making this cape more effective. That, and it also gives some nice armor and health. You sell your doran's ring for this item.
The final item is a black cleaver, this should be self explanatory as it works similarly to the malady, just more powerful and ad based. It also gives a nice bit of attack damage and attack speed to compliment it's passive. You sell your kage's lucky pick for this item.
At end game you will have 4 items that apply on hit effects, meaning that your ult is a major meat grinder, and even if its on cooldown, your W brings up your attack speed to get the stacks up with just basic attacks.

When laning with warwick, your best option is to harass the one with the least healing potential so that you can keep your E constantly active once you get it, your E and W are your keys to getting kills, therefore you should try to keep enough mana to use a W followed with a Q to pick up the kill. Warwick has a pretty high base damage and your runes help to give it the boost it needs to kill enemy champions.
If you find yourself keeping the enemy pushed behind their minions, basic attack and last hit the minions to keep your health as high as you can, this will give you a better chance of surviving when either team initiates, or I you are ganked. Warwick essentially gets boots with his E, this means that it should be hard to chase you or sucessfully gank you, so as long as the enemy team are a good bit below half health don't feel afraid to push a bit and get some last hitting done, just watch out for summoner heal or any stuns as these can turn a good push into a double kill for the enemy.
Make sure to have good communication with your lane partner because you don't want to initiate when your lane partner won't be able to do much to help you as this is just asking to be killed.
As warwick you want to be very careful when laning against assassins such as akali or talon as you do not have anything to counter them easily, mainly due to your lack of cc. If you do end up with a lane you can't handle easily, you want to focus on getting cs and staying alive, otherwise you won't make the ap to ad transition, which can decide whether you win or lose the game.
Ideally you don't want lane with your ad carry unless you want the damage from the ad carry to guarentee your E being active. The reason you don't want to lane with your ad carry is because warwick needs quite a high amount of cs to get his malady and wits end asap, if you don't get these early enough you won't be able to make the transition to attack speed and AD for team fighting, and making this is transition is crucial, i've had games where I go 3 and 0 in laning phase but didn't manage to get any more kills because I didn't make the transation. The transition is when you buy the recurve bow for the madreds, and should happen by 30 minutes in at the latest, missing this can be the difference between you successfully pushing or feeding.
A good laning partner for Warwick is someone who is quite tanky with a good amour of cc. Examples of tanks that are good partners are: amumu, alistar, rammus, singed, malphite and blitzcrank. Soraka works for a lane partner because of her mana giving ability having a similar cooldown as Warwick's Q, allowing you to endlessly spam it while having the mana to use your W and ult. But she is not advised because ww doesn't have any cc to save her, nor the damage to kill someone like caitlyn before they kill soraka.
An exampe of an initiation, with amumu, would be: you ult onto the one with the lowest health (9 times out of 10 this is the main damager as well) and amumu stuns the other one, this gives amumu about 1.5 seconds to use his W and E to do damage to them both. When they start runnig amumu should ult and stop them both. Then you use your W to kill the one you ulted onto, and move onto attacking the other one, using your E to catch up and Q to weaken them, if not killing them in the process. If this doesn't kill them then they will have to flash to get away or you will kill them with basic attacks because of the speed buff your E gives. Admitedly this tactic won't work 100% of the time, but it's an exampe where u kill 2 people while hardly taking damage because of your timing and teamwork (don't take it that this will always work as there are quite a few champions that can counter it, such as morgana, gangplank, kassadin and annie can even tibbers stun you between ur ult and amumus ult, possibly giving her a double kill).

By the time this phase start you should atleast have your wit's end, hopefully your recurve bow (most of the time I get it within 25-30mins), which is why you need good cs during laning phase.
If you do't have the items, push top a bot a bit to annoy the enemy team and get some gold, as well as maybe cause some minion pushes to take down turrets. But whatever you do, you don't want to put yourself in a situation where you're almost guaranteed to get ganked, this may seem obvious, but the amount of people I see pushing and end up setting themselves up perfectly to be ganked is ridiculous.
Once you have your recurve bow you should start pushing mid as much as you can with your team, the attack speed you have at this point is a nice amount to take out a good number of minions quickly, and the AP helps your Q to take out siege minions. You want to do this until you can afford your bloodrazor.
This is the point where you become a massive danger to the enemy team, I have easily taken out amumus without them being able to do anything to me at this stage, with all the on hit effects your ult reduces the magic resist alot, your magic resist by quite a bit and does good magic damage with each slash because of the bloodrazors. After your ult has finished, you want to use your Q on the champion you just ulted, if they live then pop your W and rip them to shreds with basic attacks. This is great for getting rid of AD carries in team fights, or for giving out revenge to those annoying backdoorers.
So after ripping down the enemy team multiple times, and pushing some lanes, you will have enough to sell your doran's ring and pick up the sunfire cape. So now you have the survivability you need to get in, ult -> Q and get out if you're focussed (if you're not being focussed then pop your W and make them wish they focussed you) as well as doing a good bit of damage to the enemy team, as well as taking out their AD carry (as you can tell, I love taking a team's AD carry away from them, they always end up so damageless afterwards). So after winning a teamfight, go straight to pushing a lane, even if you can buy your black cleaver, you will have about 40-60 seconds (depending on how long the game is) of undisturbed pushing, and your passive lifesteal and Q mean that you can't use your low health as an excuse to go back. So start pushing and take the game into the end phase.

This phase is met when you either buy your black cleaver and all the elixirs, or when you take down the first inhibitor.
At this point you are going to have a giant advantage over your enemies, you have a super minion lane and they don't. You could even have multiple lanes of super minions if your pushing during the pushing phase went well. So holding back now is pointless, the only thing left to do is to get in their base, take out all 3 inhibitors (while destroying their AD carry ofc) and swarm the nexus. Your goal is to make it so that the enemy has no hope of victory so their either surrender, or you have about 12 super siege minions around their nexus, either one has secured you the game.
Once their nexus goes boom, drop your GG and go and celebrate with your team.

Pros:
+ Great harasser early game
+ Great sustain
+ Transitions nicely between AP and final build.
+ Fairly tanky late game
+ You can easily rip tanks to shreds mid/late game, let alone AD carries
+ Build is not too expensive and only requires you to get a good amount of cs to get it rolling (of course getting fed helps speed it up, but not everyone is good enough to get fed every game).
+ Great pushing potential and damage output mid game.

Cons:
- Squishy early game
- Has trouble dealing with assassins such as talon and akali (getting a oracle's would help here)
- Insane amounts of cc will be your downfall. (I'm talking 3 stuns in a row)

Warwick can easily destroy the enemy AD carry during teamfights as they're is no way to stop him from beginning his ult on them, and it is also unlikely that they will have a silence on hand as they will have used that on your caster.
Word of adivce: Don't even bother ulting gangplank