http://na.op.gg/summoner/userName=Jester%20of%20Quebec
I main Vi jungle and I build her this way :
Stalker Blade -> Warrior enchantment -> Boots lvl 1 -> Phage -> Black Clever (Extremely usefull, you want that 20% CD asap, the HP for the passive and the armor shredding all fit Vi extremely well)
This is her core build for damages, you'll get 50 AD, 10 armor pen, 30% CD reduction, a passive that will give you mov speed in jungle and on ganks, more armor shredding and 400 HP.
Vi ult have a pretty long CD and that 30% CD (40% with blue if you have a Zed mid or something that doesnt need mana) will be extremely usefull, her Q base damage is extremely high plus it gives a knockback.
You will have less burst than with a Trinity, but your utility plus gank rate will be much higher and you'll be stronger way sooner since Black Clever only cost 2600 gold.
After these your build will have to change depending on what is on the other team, at this point you want to go with only tank items, I recommend Randuin if they are mostly AD, if they are mostly AP, in that case I recommend Banshee Veil.
You'll also want to upgrade your boots, same drill if they have magic damages or physical, plus if they have CC, everything is important.
Her power Spike should be from lvl 6 to lvl 12 (From the moment she get her ult until the laning phase is over). She's way stronger when it come to ganks and get pickup kills then in teamfight, still she will stay pretty strong since her denting blow will make her a viable option to shred tanks and she still have the damage to burst down the carries, but at this point it'll be up to your judgment. If your carries are fed I strongly recommend that you peel them, with your Black Clever and Denting Blow you'll be able to take a lot of their armor and your ADC will be able to take them down a lot more easily.
There's 2 way to engage with Vi, Q -> 1 Auto-attack -> E -> R, this will require dfrom you a fully charged Q but you will do a ton of damages, I recommend that you wait for the flash before ulting.
Next is an easier engage but also a long range engage.
R -> a fast non charged Q -> 1 Auto-attack -> E
This one will do less damage but it's good if they saw you coming, if you got a Yasuo with you or something with lots of damages it will probably be your best options especially if you go bot and do a lane gank.
Vi is a high mobility Bruiser with these 30% CD, this means you should be able to invade the ennemy jungle if you have vision of their jungle.
Also Vi is a pretty strong 1 v 1 champion early, with her passive you should be able to take down drag in solo at lvl 5 or even lvl 4 with 2 or 3 hp potions. (recommend that you upgrade denting blow to lvl 2 if you want to get a solo drag, don't max it first though, lvl 2 will be enough)
I also recommend that you upgrade your trinket at lvl 9 for the green upgrade, it's better than a sightstone for only 250 gold, as the Jungler you should always put one ward on Dragon and Baron, with your high mobility this shouldn't be dangerous, plus you can 1 v 1 almost any jungler, of course if you're against a fed Xin Zhao or something like that I recommend you Q over a wall and flee as far as you can.
Edit : You should never go with Cinderhulk, yes her passive stack with HP but it's only 10% and the CD is still pretty high even at high level, so unless your team really need a full tank (Because Ori mid, Yasuo top, Nami support, or a team comp like that) you should never go with Cinderhulk, since Vi base damage is extremely high, you want that Warrior enchant to be able to destroy your ennemy when you gank.
is good but it gives you a lot of stats you might not need (movement speed, ap, crit chance)
-- which gives you both true dmg and dmg reduction [useful for 1v1]
is also a good choice. Gives you HP (for bigger blast shield) and the armor shred works well with your denting blows
(can replace tabi with mercs if needed)