The following are totally armchair guesses as to how to play Volibear. Most of my research has been conducted watching videos of high elo players evaluating the character during play and the experience I have playing him.
It should be noted that the information provided in this guide should be taken as a guide lines only. No one is telling you to to this or you are a noob or whatever passes for a poor player insult these days, it is just an attempt at sharing some of the more successful experiences I have had with the game while playing Volibear.

Thanks for taking the time to read the guide. If you found it helpful or if I made mistakes (its my first guide) feel free to leave comments and votes. Thanks and gg!

Volibear is a Tank/Tanky DPS character. He doesn't have a lot of stuns and his CC is passable at best. He has a little flip and a decent slow, what he makes up for is HP and Item Support to be a walking wall that can bite your freaking face off. So that said HP>Armor>AP and you will likely have a pretty decent build all the way around. In terms of play style he can be used very well as Solo Top when he isn't the Jungler. As the Jungler he's a passable ganker and is a definite threat throughout the mid game.

I rune for HP and Speed and a little Armor Pen for late game

3 Marks of Alacrity for Attack Speed for your W
6 Marks of Desolation for Armor Pen
9 Seals of Vitality for HP to stack on your W
9 Glyphs of Alacrity for more Attack Speed for your W
3 Greater Quints of Fortitude for a Flat HP for early game again for your W

Volibear is all about damage and the threat of a big finishing bite maximize these and you are cooking with fire.

I have Volibear rocking a 9/21 Configuration

9 in Offense maxing the early damage ability - Brute Force and a point in Butcher for added minion damage.

I also max out Alacrity for attack speed for synergy with the W and then take a point in Weapon Expertise for added late game Armor Pen

Volibear is pretty flexible in Item Selection.

Jungle Build Core are

Ninja Tabi - For early Armor
Wriggles Lantern - Utility and Lifesteal
Warmog's Armor - HP

Tanky

Spirit Visage for more HP and MR
Sunfire Cape for HP and Armor
Shuyra for Utility and CD Reduction as well as HP

Tanky/DPS

Spirit Visage
Sunfire
Atma

Optional

Defense -

A lot of AD - Thornmail
A lot of AP - Veil

Offense

Trinity Force - Good all Around
Rylai's Crystal Rod - Great W and Slow Effect as well as HP for your W

Pros

Lots of HP and Passive makes him pretty tough to kill when built well
HP and AS stack on his Frenzy Ability
A little AP makes him a scary Tank able to Super Slow Team Fights
Good Burst and Finisher

Con

Seems a little slow of an initiator
His Flip is a littler short
He can be out run
Limited Range
Mana issues in long team fights

Jungling is pretty simple

Wolves>>>Blue>>>Wraiths>>>Golems>>>Red

At that point you should be 3 with both buffs and ready gank Bot or Top depending on the situation.

You can prolong the jungle phase by Picking up the Wolves which will have popped again and then the wraiths after that you will be 4 and can pick up Wriggle's.

From my perspective the basic skill sequence is Q>>>E>>>W

The Q is a flip which sends the guy behind you and likely into a teammate and then the E is an AOE Slow for Champs and a fear for minions which will buy you some breathing room to land your 3 frenzy strikes which is your finisher and big damager. You can save the W after more than 3 strikes as it scales the damage as a % of what is missing from the targets HP + a % of you Bonus HP value.

In the Team fight blowing your R will give you a on melee strike chain lighting affect that is a percentage of AP very useful if built in to. Rylai's makes this even doubly effective as your AoE E slows x2 now.