My comments on the abilities require you to already know what's written in the tooltip, so read the ability-tooltip first. I will only give additional information, helping you to adequately understand and use each ability.
If you are new to the game and don't know how Warwick works at all, just enter a training game, read his ability-tooltips and try everything out for a bit.

Passive Eternal Hunger:

Gives us a nice upgrade to our insanely strong duel-potential. Also giving us the opportunity to heal up in the jungle when we get low on health. Eternal Hunger together with Blood Hunt allows Warwick to easily solo-kill Dragon in the early game, too. (Cloud Drake can be hard at early levels (attacking very quickly) while Mountain Drake is the easiest one to kill due to his slow attacks).

Q ( Jaws of the Beast ):

There are 2 possible ways to use Warwick's Q Jaws of the Beast. For the first one, you just tap "Q" on your keyboard and release your finger from the key right after the tap. Doing it this way, Warwick just leaps forward and performs his bite. Nothing special happening here.
The second way to use Jaws of the Beast is to press the "Q" key on your keyboard and keep pressing it for longer, causing Warwick to dash through the enemy and appearing behind him. While Warwick "dashes" through the target, he is immune to any displacements (knock-ups, knock backs; e.g. Blitzcrank/Thresh hooks, any airborne abilities etc.). In addition, if the enemy performs a movement ability while Warwick is dashing through the target, Warwick will follow the movement and still appear next to the enemy, no matter where he went. This works on almost every movement ability in the game, including Flash, Blast Plant, Bard Tunnels ( Magical Journey), Ryze Ultimate ( Realm Warp) et cetera.
You always want to use the second way of pressing "Q" when ganking, so you will follow the enemy's Flash if he uses it.

W ( Blood Hunt ):

Tooltip explains it. One thing that isn't in the tooltip and lots of people think it's a bug (it's not, Riot wants it to be this way, otherwise the ability would be too strong):

When you die and later get back to life, Blood Hunt will not automatically search for low health enemies and trigger on them. They need to take damage from your team while you are alive to trigger Blood Hunt (minion hits and tower shots work as well)[/list]

E ( Primal Howl ):

Tooltip explains it. Try to use Primal Howl when the enemy is trying to burst you down, to avoid as much damage as you can. Also when ganking, try to activate E ( Primal Howl), then Q ( Jaws of the Beast) behind the enemy and then re-activate E ( Primal Howl) to make the enemy run towards your allies when he gets feared.

R ( Infinite Duress ):

When Warwick performs his R, he is immune to EVERY(!) CC in the game while flying through the air, not only to knock-ups/backs but also to stuns et cetera.
Easy example: Twisted Fate is throwing his stun card ( Pick A Card) at you while you run towards him. You just press R when the card is flying and it will hit you while(!) you are jumping, making you immune to the stun, applying your R's damage and CC to him.

If you use your Q ( Jaws of the Beast) and R ( Infinite Duress) the right way, you can deny almost infinite amounts of CC from the enemy, giving Warwick insanely high outplay-potential. Getting into playing Warwick is easy, but his skill cap is very high, making him by no means a "noob champ".