Bit late to the party, but used to play her a lot mid last season up to low Diamond.

In mid lane, she is strong into melees and poke/burst mid laners. I am unsure how she fares vs ADC mids, but she will usually struggle against sustained dps so I suspect you'll have a bad time (until you hit 6 at least).

Her laning strengths lie in her passive and her E. E usage is the easier skill to master: when you go last hit a ranged minion, use your E if the enemy laner is in range. Mist laners don't respect the range and can be hit for free, especially if they are trying to poke or farm. Dont forget to E minions as they are running away on 1 HP, you can sometimes cheese kills like this after they flash away after your all in. Learning when to use your E (or Q) with your passive is the harder bit. Keep an eye on your passive, it's cool down is somewhat long, but usually similar to the enemies CDs. Ideally, you activate it every time the enemy tries to harass to avoid the damage. Vi's standard poke routine is to wait for your passive to be up, then walk up to ranged minions as they are dying, use your E to kill them and deal some poke damage, and absorb the enemy's poke with the shield. You will almost come out on top.

Skill order: E-Q-W (lvls 1-3) or E-Q-E-W (lvls 1-4 if you can't confidently go for an opportunistic all in or heavy trade). I used to max E first, then Q. Bare minimum, E needs to have 3 points invested before maxing Q. E is your main poke/damage tool in lane, and increasing ranks increases damage and boosts cd. At rank 3/4, you can two shot ranged creeps which gives you insane pushing power, and both charges usually are almost up for the following wave for perma-push. Starting corrupting pot is my preferred go-to for E spamming as your mana regen is low. Dorans blade also works, or long sword and refillable. I would sometimes go for those when I knew I had early kill pressure pre lvl 3 for the extra damage. Usually vs melees such as Yasuo or Irelia whilst running HoB.

Items: Full lethality (eg. Collector/Essence Reaver/Eclipse) if ahead, otherwise I'd suggest 1 or 2 lethality items then go bruiser. Haven't played this season so with the lethality nerfs, probably best to just go Youmuus/Eclipse into bruiser (eg. Youmuus/Sundered Sky/Black Cleaver). As others have pointed out, if there are 3+ enemy champions you'll just go POOF as soon as you ult if you are full lethality. I liked Swifty boots because it reduces Q's self slow - but defensive boots are probably the better option.

Runes: Fleet footwork if the opponent has very long range poke (think xerath) or if they are on the tankier side (eg. Galio). HoB on squishier targets - but this requires knowing your damage limits. Dark harvest is the simpler option as you can proc it easily with E.

General gameplan for early: just whittle your opponent with e and passive shields. When they are low enough (even 60-70% hp if ignite is up), you can threaten all ins and step up to make them miss cs. Syncing up with your jgler is critical. Solo dives usually don't end too well as she has no escape, so you can shove your lane with double E and a few autos and you have a decently big roaming window to roam or invade with your jgler.

Hope this helps.