Volibear is a brand new champion to LoL and the guides will surely come pouring in. As it is still relatively early for him I thought I would give writing a guide a go.

Think of Volibear as a tanking disruptor with Tryndamere style (not level) damage, Singed/Rammus utility and Cho'Gath amount health/active burst.

Pro:
Ridiculous survival. With this build you will end up around 4k health so your passive heals for around 1,200.
Incredible disruptor with a combo of flinging and slows.
Easy to get kills as his W does insane damage as it scales with his health (might get nerfed?)

Con:
Slow early game... Really slow. A skilled ranged will make your life hell in the early game.
This build is VERY expensive. If you don't get your Warmog's Armor early it may be difficult to compete.

I have built this champion as an AD tank. His slow and ultimate may scale with AP, but his W scales so much better with AD and health while making him even harder to kill.

Attack speed is to make certain his W is available at all times and to make his end game damage bonus from Atma's Defender even more effective. W increases increases your attack speed so the more basic damage you can do, the better. By the third hit Volibear hits as fast as lightning. {hah?)

This guide is very expensive to follow. I personally go with Avarice Quints to increase passive gold. You could also go with passive health Quints to increase his early game damage and hopefully get a few extra champion kills in the early game.

This guide points Volibear into almost becoming an AD carry and as such he focuses on attack speed and health to increase his W's active and passive use.

This guide focues on using Volibear's W to get champion kills so it should be the first maxed skill. As his E and R scale with AP they will only be used as utilities to set up kills with W. Max his ultimate whenever possible. After that max W first to get the largest hit possible and then alternate Q and E to add increased damage and lower cooldowns.

As Volibear is a tank when it comes down to it you should likely have Teleport. This enables you to jump into the action as quickly as possible.

Ghost is used as Volibear's escape and chase mechanic. His damage is built upon white damage and usage of W so Ghost allows him to get as many basic attacks and activated Ws as possible.

If you're jungling I would get Smite instead of Teleport.

The build focuses on Volibear's auto attack damage, health and bonus damage from his health. To do this most items have health on them. The two first items are important simply because they add much needed regen and increased gold earning.

By the end depending upon your enemy you can switch to a Banshee's Veil instead of Shurelya's Reverie if you need the added magic resist. Otherwise Reverie's utility and regen is more useful.

The Wit's End is a debatable item. The added attack speed further increases your basic damage while making your W more quickly accessible in a new fight. Also the added magic damage is a nice addition to what is dominantly a build focused on physical damage and attack speed. If you would prefer more survivability, but less damage I would suggest a Force of Nature.

Volibear is great tank and initiator. Generally do not start fights alone, but with your team behind you be aggressive enough to initiate by focusing a carry and tossing them back to your team.

Obviously if your own carry is being chased, remember you can AOE sloe AND toss back an individual target giving your teammate valuable time to escape.

This guide is a work in progress and I'm sure it will be criticized for its short length. This is still a new character and as such it's all a bit of a guessing game still. I have fairly good luck with this build as I'm tanky and still threatening due to my large burst from W and how much I can control the enemy's position.