So, you want to play an armored bear?
Good. You've come to the right place. The Riot team has been talking about armored bears for a while, and for a good reason. They're OP. Bears are known for easily separating a fool's head from their bodies.

This Champion has come out very recently. So I will update this guide as time goes on.

Pros:
Can obliterate people.
Nice early game with my runes.
Can gank fairly easy.
Has decent crowd control.
Has a couple ult-like abilities.
Is a bear.

Cons:
All abilities are very short-ranged.
Can be kited.
Because Volibear is a bear, the opposing team WILL focus you.
Not a very good escape mechanism.

The marks are for a little bit more damage on your auto-attacks.
You could exchange these for attack speed or attack damage.

The seals are for tankiness, he is a bear after all.
These can be exchanged for health, the health will also boost his W.

The glyphs are for tankiness towards casters.

The quintessences can be exchanged for attack speed, attack damage, armor, or magic resist.
The health is excellent for early game tankiness with his seals and glyphs, and also boosts his W, Frenzy

The 9/21/0 mastery setup works very well with his runes. The masteries compliment the runes. You get extra armor, magic resist, and health.

You could switch it up and run a full-blown offensive mastery tree.
Be sure to grab all the AD stuff in the mastery tree. I would use the remaining points in the defensive tree.

I always like to start out with a Doran's Shield
You can exchange this for a Doran's Blade

I then would work up to a Phage and Mercury's Treads
The phage for health and attack damage. The boots for running like you don't care.

Frozen Mallet] is useful for chasing people, and the extra health and attack damage. The slow is great on Volibear. He can chase down people and pop his [[Rolling Thunder to get the champion back where everyone can kill him/her.

Warmog's Armor for the extra health. The health really helps his W, Frenzy

Atma's Impaler: Now you can turn all that health into lovable attack damage and REMAIN tanky.

Bloodthirster: This will eventually give you an extra 100 attack damage, and some great life steal.

Trinity Force can help you with damage throughout a team fight. You can also exchange this for a Phantom Dancer so you can chase more, and hurt more.

I get Thundering Smash first, so my lane partner can really help with getting first blood, so I get it first. Keep in mind the 45% speed increase is only applied when going TOWARDS a champion, not running away.

The goal is to max out your W, Frenzy as fast as you can, this is one of your ultimates, it's just about as effective at higher levels of health and rank as Garen's ultimate, Demacian Justice.

Your E, Sky Splitter is very great at slowing people, not for damage. That is why I max it last. The fear on minions and monsters is cool though, use it in a minion wave if they're damaging you. A good example is if you are harassing an enemy champion, the minions will switch to you. Instead of running in a bush, which may take longer, you can run in the middle of the group, and fear them. Sometimes this may help if you kill a champion, but then are about to die from minions. The fear will give you a bit more time.

Your ultimate, Stormbringer is very great in teamfights. The lightning will arc across everything. It's great for clearing a minion wave while killing a champion, or killing a minion wave while hurting a champion. It lasts 12 seconds, a very long time.

Your passive, The Relentless Storm is a passive much like Mundo's ultimate. If you buy a Spirit Visage your passive will heal you for crazy amounts. Don't rely on your passive to save you though, if you tower dive someone, you have a chance of not healing enough. Think of it as a life saver, not an ability you need to depend on.

I use Ghost and Exhaust for very good reasons. Exhaust can save you, or help you kill something else. If some AD champ is trying to kill you in a 1v1, or is leaving, don't be afraid to use it on them. Use it wisely though, I said earlier in the cons that you don't have a great way of running away.

Ghost is useful for chasing something, but I find it more useful to run away. Volibear is prone to ganks. The speed boost on Volibear's Q, Thundering Smash only applies when going towards an enemy champion. Ergo, Volibear is weak on escape, but very strong in crowd control.

Hope this guide helped you a little.

I will update this guide more the more I play Volibear