Hi I'm Blissful Totem, and I'm a main jungle player. I'm not the best player in the world, and wouldn't claim to be but this is my preferred build on my favorite feisty jungler, Vi. This build has helped me climb the ladder bit by bit in the current Season 4. I'm currently sitting at Gold V, but am working hard to continue climbing. I don't want to bog you down with a mass of text, so I will go over the basics of the champion in a short sweet manner.

Pros:

Early Game Dominance
Level 6 is an instant kill
Good mobility
Objective control with high damage output
Strong Dragon slayer
Can delete squishies in teamfights

Cons:

She can peel, but isn't the best at it
Initiate before 6 is skill shot based
Can become just a minor nuisance if behind

Armor penetration reds will increase damage done to the camps via all your skills, but the main purpose is for the added damage it gives to your ganks. AD reds serve the same purpose increasing clear speed and early power.
Armor yellows are a general staple for junglers. It reduces the damage of the camps significantly , and will help survive ganks on AD champions.
Magic resistance blues another common staple for junglers. The flat blues allow for early defense against magical damage, and the scaling ones keep your starting magic resistance relevant until you buy an item to provide more.
AD Quints serve the same purpose as our reds. Clear speed, and overall dominance of your enemies. More armor penetration being unnecessary because of your denting blows ability, and the fact that you will be rushing a The Brutalizer.

When Vi's activated abilities damage an enemy, she gains a shield which absorbs damage equal to 10% of her maximum health for 3 seconds.

Her passive provides her with added survivability in team fights as well as while doing early jungle clears. Activates when a skill hits a target, and if used properly can't help you survive various things including low health ignites if you can find a target to quickly strike.

FIRST CAST: Vi begins gathering energy into her gauntlet, increasing damage and dash range over 1.25 seconds. While in this state Vi cannot attack or use her other abilities, and her movement speed is slowed by 15%.
SECOND CAST: Vi dashes towards the cursor's location, dealing physical damage and applying Denting Blows to all enemies hit. Vi stops upon colliding with an enemy champion, knocking it back. Vault Breaker deals 75% damage to minions and monsters.

This ability alone is one of Vi's most important skills. It provides high utility in the fact that it can be used to move about the map quickly, it provides great initiation and slight CC on contact, can activate her passive, and also provides absurd early burst when maxed. Can be used in conjunction with Flash or Cease and Desist to initiate from great distances or catch up to running enemies. You also have a reliable form of escape in most cases since you can jump walls on a low cooldown with this ability, but there is one huge weakness to using it. If you hit a champion you're not going any further so if you can't make a reasonable distance, or path to travel through you could very easily run into the target you are trying to escape from and go nowhere at all.

PASSIVE: Every third attack on the same target deals additional physical damage equal to a percentage of the target's maximum health, reduces the target's armor by 20%, and grants Vi bonus attack speed for 4 seconds. Denting Blows deals a maximum of 300 damage against minions and monsters.

Denting Blows allows for a quick early clear with the percentage damage, on top of the aspd boost, and armor shred making those big buffs squishy children. The higher the level of this ability the higher the percent damage, and aspd increase allowing you to have your way with any jungle objective. The more you level it the quicker, and more easily you will tear targets like dragon to shreds allowing you to sneakily solo it then leave the dragon pit using your Vault Breaker. Since this ability is also applied by your other abilities except your ultimate along with auto attacks it can add surprising burst to your ganks with just a Vault Breaker Auto-attack Denting Blows.

ACTIVE: Causes Vi's next basic attack to deal increased physical damage, hitting all enemies in a cone behind the target. Vi gains a new charge of Excessive Force periodically (this reload time is reduced by cooldown reduction) and can hold up to 2 charges at once.

Now many people for some reason max this ability first, but there are a few reasons why you shouldn't. The main purpose of this ability is to help you apply the Denting Blows in a quick burst. The damage only goes up by 60 between first and last rank, and the cooldown for charges goes down by 6 seconds making it go from 14 to 8 seconds per charge. As the game goes on you will find that you have plenty of charges because you don't need them as much for the jungle, and the other abilities just help you much more with objective control and map pressure. Even though you do not max it, it does have its usefulness though. As previously stated it can help apply Denting Blows quicker, it increases your attack range from 125 to 175 if you just can't reach a target. It can also be used on a minion to hit a fleeing low health target possibly securing an otherwise lost kill.

ACTIVE: Vi targets an enemy champion and chases it down. She performs an uppercut upon reaching it, dealing physical damage and knocking it up for 1.25 seconds.
While charging, Vi is immune to crowd control and will knock aside enemies in her way, dealing 75% damage to them.

Once you gain this ability at level 6 going into a lane with it almost guarantees that you will achieve a kill for yourself or the lane. It is great for chasing down those fleeing targets, and even initiating opening a line through your enemy team by knocking them aside so that you can reach those lovely squishies. You have to be careful about how you use it though because once you use it there is no cancelling it. Using it on a champion such as LeBlanc can land you in the worst places possible including a fountain if used in the base. It can also serve as a form of peel to remove those pesky assassins from your own squishies instead of initiation allowing your team to continue pouring out the damage while protecting them.

Your role in a teamfight will generally be that of the AD Offtank. You can use your Cease and Desist to grab hold of targets such as the ADC with no one being able to stop you, and depending on how far ahead you are you can usually instantly delete them from the fight making it a 4v5 in the blink of an eye. This is sometimes not your best option though. If the enemy team has the ability to do exactly what you can then you will want to sit on the front line keeping people out with your Vault Breaker or using Cease and Desist to grab hold of those nasty assassins going for your ADC.

As the fight starts to thin out your Denting Blows paired with a Black Cleaver can leave the more tanky targets susceptible to the physical damage that your own ADC will be pumping out making it as if they weren't tanky to begin with.

You can fill the role of a defensive guardian protecting your team, or the ruthless initiator that rampages the enemies squishies. It all just depends on what you can get away with based on the enemy team.

Be careful of champions such as Thresh and Janna whom both have abilities being Howling Gale and Flay which can stop your Vault Breaker dead in its tracks. Vi is not quite as susceptible to kiting because of her Vault Breaker unlike many other melee champions, but any form of CC can cancel that charge other than slows.

In conclusion Vi is a very powerful champion staying useful throughout the entirety of the game. Early and Mid game she is powerful and destroys targets with ease. She also destroy objectives with ease including jungle monsters with her Denting Blows, and towers with her Relentless Force. Her late game is nothing to laugh at either, she stills tears apart objectives with her now maxed out Denting Blows, she is hard to keep hold of with her Vault Breaker, she can back door like a champ using Vault Breaker and Relentless Force, and also has powerful team fight capabilities. She is in many ways like Jarvan IV seeing as she can fit into many team compositions with relative ease, and has such powerful long range initiation/chase. Her ganks can be a bit dicey against other highly mobile champions since she is skill shot reliant before level 6, but managing to hit them and your own teammate following up on this will generally guarantee a kill because of her burst. Overall Vi is a fun champion, and really strong with the current meta. She can farm the jungle quickly, and provides the damage of a carry with the tankiness of an Alistar using Unbreakable Will. As always aim to have fun with your champion, and best of luck to all in solo queue. I hope this guide helped you in some way.