Volibear being my favourite champion I've came to adopt a set build with only a few alterations required.
I'm no competitively ranked player but I have a highish win rate as volibear and even when I lose I generally get even KDA.
I recommend reading this guide and not relying on just going with what the above build says, with all tanks you need to adapt your build to match your opponents strengths so you can keep supporting your damage dealers.

I've taken the 9 attack speed marks for the 3 stacks of the W passive and the on-hit damage of the Madreds.
I've taken the 3 attack damage quints just for extra damage in the jungle, this can be swapped out for health, magic resist or armour quints but I prefer the small damage boost since I build tanky items for the most part.
The 9 armour seals and 9 scaling magic resist glyphs are pretty standard. Its up to you about whether you want flat or scaling magic resist but since the jungle is predominately AD the early magic resist isn't necessary.

The defence tree is an obvious one, I was picky with which ones I wanted so I could spend them in other areas so I ignored the tiny monster damage reduction etc.
I took the one utility mastery because that 1 second off recall is nice, and the extra attack speed and cooldown reduction from the offensive tree is useful in the early levels.

As I previously stated Volibear's item set is interchangeable.
Lets assume the default build (not counting level 2 ganks) is:
Wriggle's Lanturn + Boots of Swiftness HG + Frozen Mallet + Wit's End + Randuin's Omen + Spirit Visage.
Now it's obvious that if the enemy team is low on AP then aiming for Randuin's or Sunfire after Frozen Mallet is a better option. Similarly trading Wit's End for Black Cleaver could be more profitable.
Very late into the game you should swap out Wriggle's Lanturn for either Guardian's Angel, Warmog's Armour or Trinity Force.

NOTE: Level 2 ganks should be a Cloth Armour start not Machete! Read "Skill Sequence" for Level 2 gank guide.

The Frozen Mallet is Volibear's key item which makes his ganks much stronger, gives his W active a stronger bite and is an all-round strong item to get.
Wit's End is another key item due to the added magic damage and magic resist stealing the items gives, the attack speed is also a very effective stat to have due to the indirect scaling with your ultimate.

Start with E, then W, then Q starting at blue buff. The E fears the monsters and gives you free time to attack them, the W for the added attack speed and bite, and the Q just finishes the skills to get ready for a level 3 gank if the opportunity arises.
Keeping the W either the same or higher than any other ability and pushing other skills based on needs of the team and for ganking.
Aside from the first 6 levels, levelling order isn't really specific. Volibear should level what he needs to gank when required: if the enemy is mobile levelling up Q earlier makes ganking easier, if the enemy can escape from you after you gank try levelling your E earlier, otherwise just up the W for the passive for farming.

A level 2 gank you either start with W or E and proceed to take Q at level 2 and rush in. Preferably if the opponent has poor escapes or little CC, and with an ally with either high level 1 damage or early CC. Avoid ganking AP champions due to the poor starting magic resist!
As volibear its wise to go Red buff and early gank the lane nearest to the buff (top or bot) for the on-hit slow and true damage DoT, but starting blue can work too if the opponent to gank is easy.

NOTE: With one ally, you should be able to take Dragon at level 6/7 with your passive to proc, just watch out for enemies!

Volibear needs successful ganks, working with a CC heavy team aids this very well.
Without a hard CC setup ganking champions like Lee Sin or Vayne is almost impossible because of their numerous escape abilities.

Chosen of the Storm:
Don't be afraid to lead the charge in team fights, assuming they don't have a lot of hard CC and/or your team mates can't cover the distance. However in the middle of a fight your passive will keep you alive a lot longer than your enemies will expect, this makes the opponents underestimate Volibear, plus the added 150+ damage on-hit chaining onto 3 other champions from the ultimate can turn an even fight into a crushing victory.

Rolling Thunder:
Volibear's speed up and fling, Volibear's only hard CC. Rolling up to a champion with Ghost on can force flashes in the early game which indirectly gives your team the advantage, coupled with using the Majestic Roar mid-run to slow them down as you catch up to them can sometimes save you from losing your Rolling Thunder.

Frenzy:
A very good farming ability, an ability I level up solely for the passive effect with the active being an added bonus. This ability scales with itself, each hit for 3 hits increases your attack speed which gets you the active available sooner, but the real strength to the W is the indirect scaling with your ultimate to get more hits off.

Majestic Roar:
A fairly standard AoE slow with an added minion/monster/pet/clone fear. This skill is a crucial part of Volibears kit with both jungling and ganking.

Thunder Claws:
This ability is Volibear's second hidden power. Enemies will underestimate your overall power with a super-fast health recharge and a powerful on-hit damage boost.
With some teammate assistance Volibear is almost unstoppable when ganking at level 6.

Pros:

• Strong Tank
• Surprisingly high damage output
• Fairly easy to gank with
• Scales well into late game

Cons:

• Heavily teammate reliant
• Weak vs CC
• Weak vs easy escapes
• Can be problematic if counter jungled