Vi is an incredibly strong early game jungler. She is also a better than average duelist, making her an ok pick for toplane. Most of the time, you will want to be playing Vi in the jungle. Here is a quick guide for clearing the jungle with Vi.

There are two main paths you will want to take when starting red side. Pick them based on which side you want to get an early gank on, bot or top.

For a botside gank, start with your red buff. Try and kite the monster towards you raptors, and use your e along with your smite to take out the big raptor asap. Cleanup on the little guys is easy enough, but try and kite them down to the top wall of the red buff spawn. Kill your krugs, then look for scuttle. Once done, you want to look for a gank opportunity either botside or midlane. If none are an option, you may look to invade, however, keep an eye on your mid/bot priority to make sure you don't get collapsed on if the enemy jungler shows up.
The second path is if you want to hit level 3 ASAP and gank top. Start your red buff. Kill the raptors, then beeline for your wolves. Kill both small wolves and leave the big one. This should get you level three after you kill your blue buff. Get the scuttle, then gank top or mid. Again, you can look to invade if these options aren't available.

Remember, Vi is a stronger than average duelist, even at level 3. If you happen to run into the enemy jungler while contesting scuttle or invading, 7/10 times you will be able to come out on top of the fight. Just make sure you don't get collapsed on.

Vi has an unreal ability to control major objectives. At level 4, she has the ability to solo drake, given she has her tier 2 jungle item and at least a dagger/long sword. Reaching level 4 before the drake spawns at 5:00 in is easy. You can take the drake as early as 5:20 as long as you don't get interrupted. Make sure you have good vision on the river and behind the drake pit. But a pink ward and use your trinket to get a ward in the pixel bush. Remember, even while tanking drake you can still win fights so long as you are above 75% hp. If necessary, have your bot/midlane help you with the dragon. Take them as soon as they spawn.

Vi has a few gank options.

If the lane you are attempting to gank has a root, you want to walk into lane before charging your q. Your q gets interrupted by roots/silences, so try and avoid wasting the cooldown without getting the damage/cc off. If you have ult up, ulti the cc away and follow up with a q to maximize the time the enemy is cc'd.
If no cc in the lane, charge up your q before showing yourself in lane. Land your q and follow up with a full combo. As long as you and your laner are in sync, at least 80% of ganks should result in at least one kill.

Vi has a kit of abilities that synergize with each other very well. Your combo you should use 90% of the time you are fighting, whether it be a champion, monster camp, or an objective, is the same. Q auto E auto E. The other combo is a bit trickier. R auto e q auto e auto. Neither of these are hard. At all. These are easy combos that flow right through the entire time. As long as you can land your original ability, you can combo right the way to diamond 1.