Chosen of the StormChosen of the Storm is a great way of baiting enemies to overcommit in a fight to kill you. It heals a lot in a fairly short amount of time. However, note that it is less effective against burst damage.
Frenzy deals additional damage based on the enemy's missing health; due to this fact and its high cooldown, it's better to use it to finish off an enemy rather than initiating with it, since it scales better later in the fight.
While jungling with Volibear, you can use Majestic RoarMajestic Roar to fear minions in the middle of their attack animations, thereby cancelling that attack. While this may make only a small difference with one camp, this may be more significant if kept in mind throughout the whole path, especially against the slow attacking Blue Golem. Also you should always use Frenzy after smite or when a monster is at half-health, as it deals additional damage based on missing health.
When building offense on Volibear, it is important to remember that Thunder ClawsThunder Claws scales well off of attack speed and that Frenzy is much easier to trigger the faster you can get three attacks off. This means that building attack speed as your offensive source is very profitable.
Wit's End is one of the primary offense items for Volibear, as it gives both good offense and good defense, allowing him to serve both his primary roles.
Ionic Spark is another good choice as it adds a fair amount of health and a good chunk of attack speed. Fun factor aside, the chain lighting proc alongside Thunder ClawsThunder Claws also grant substantial AoE damage in teamfights.
Zeke's Herald is a viable build option for Volibear. The health gives Volibear more durability while boosting the effects of Frenzy through the health and attack speed bonus. The attack speed and life steal aura can help your teammate during a teamfight.
Volibear greatly depends on having high amounts of health to add damage to his Frenzy. Items such as Madred's Bloodrazor and Kitae's Bloodrazor are great counters ONLY if you build magic penetration or the opposing team does not focus a lot on magic resistance; their magic damage is based on the target's maximum health. Otherwise, it is rather expensive and might not be too useful overall.
Deathfire Grasp also works quite well at the beginning of a fight, as its damage is based on 15% of the target's current health and an additional 5% for every 100 ability power.
If you see Volibear charging at you with Rolling ThunderRolling Thunder, and you know that you will not be able to prevent being hit, it sometimes can be a good idea to move to the side shortly before he hits you. That way you do not get thrown into the direct opposit direction of your escape route, which sometimes can give you the inch you need to survive.
If you got hit by Rolling ThunderRolling Thunder, you should quickly decide if you can choose another escape route instead of your initial one. If you can, you do not have to run past him and receive less hits.
Volibear's abilities may seem like they are good at chasing champions, but because they have long cooldowns and because they are all melee range, he cannot keep up an extended chase. As long as your tank absorbs the initial burst, Volibear is fairly vulnerable to kiting.
Try not to let Volibear get gold / fed early on, if he does, he will be dealing high amounts of damage and at the same time very tanky, so your team will be destroyed as targeting him means focusing the tank, but at the same time, not focusing also means ignoring the damage dealer.