Early game:
Early game you want to play super aggressive. try to prevent your enemy laner from farming. If you can get them to half health, your all in at level 3 will kill them.
When you smell somebody with your w, as long as you aren't pushed in, feel free to follow the trail and get an easy kill. You'll be surprised at how easy they are.

Mid game:
You are your team's "cleanup crew." CC is your worst enemy. Remember, both your damaging abilities are dashes, so avoid roots at all costs. If there is someone you pick up with your W away from their team, kill them. If there is someone with a bounty that is low health at all, kill them. You need as much gold as you can get.

Late game:
You fall off late game, so try to secure objectives. You are still incredibly bursty, so if you need to you can take out a carry to help your team win a teamfight. Even without smite, you can solo epic monsters easier than warwick jungle.

Why the runes?
Dark harvest synergizes with your "cleanup crew" playstyle. Since your w notifies you of people below half health, it's easy to roam and pick up a cheesy kill.

Sudden impact is optional I use it because all your abilities deal damage after a dash.

Eyeball collection has no special synergy, feel free to trade it out however you like.

Ravenous hunter could be swapped out with ultimate hunter if you want to ult more, or relentless hunter if you want to roam faster. It all depends on your playstyle. I use ravenous because all the sustain makes you really, really tanky for how much damage you do.

Celerity is to once again compliment your "cleanup crew" playstyle. It allows you to roam faster, and will likely make dives easier.

Manaflow Band is optional but helps to let you play aggressive in the laning phase.

You rush Lichbane because your two damaging abilities (q and r) apply on-hit effects. This causes your q to do insane damage and your ult to get some ap scaling.

Next, you buy Hextech Gunblade. Gunblade adds damage to your q, and since it gives ad, adds to your ult as well. This also means that your abilities heal you more than the damage they do, so each q will heal you to full health, and don't get me started on the ult...

Boots are up to you. Movement speed helps and so does magic pen.

After this, it's more up to you. Nashor's tooth adds to your dueling and makes your ult do a lot more damage. Luden's makes you even more bursty. If you need some tankiness, you can buy a spirit visage. Most ap items work well on warwick.