I've played nothing but Vayne for a long time and climbed a lot of elo just using her. With my current 106 Ranked Games on Vayne alone I have a good KDA of 8.2/4.8/6.2. She's my favorite champ to play and I hope I can help someone out.

Pro's
-Late Game Hyper Carry
-Great at Dueling
- Tumble helps you dodge skill shots
-your Condemn can help peel or disengage
-Extremely Fun to Play!

Con's
-Sub par Early Game
-Short auto attack range
-Auto attack reliant champ
-Not the easiest ADC

All are the pretty basic ADC Setup.

Passive: Night Hunter
This allows Vayne to hunt down people who are trying to run. Be prepared for your opponent to possibly turn back on you to fight as he/she may know they aren't getting away.
Tumble
This little beauty allows Vayne to do what she do. Use this to harass in lane, get a quick 3 stacks on Silver Bolt, Chase down your enemy, Dodge skill shots, and to use with your Final Hour to go invisible.
Tip: You can Q out of J4's Ult.
Tip: Your Q will also reset your auto attack. So use it after you see the animation for another quick auto
Silver Bolts
Silver Bolts do True Damage to targets after hitting the third stack. This is great damage in all scenarios but especially nice vs tankier opponents as an ADC.
Condemn
This allows you to stun someone against a barrier/wall to dish out more Silver Bolts procs thus doing alot of damage. This is in conjunction with Final Hour makes her great at Duels.
Final Hour
This increases your damage and allows your to go invisible when you Tumble. You also can chase down enemies much easier with this activated as it also increases your Passive movement speed.

Early
You'll want to buy Doran's Blade, Health Potion, and a Stealth Ward. Just a typical ADC Start.

First Back
You'll deff want this item. Gives you some good lifesteal/damage and allows you to start getting kills in lane with the Active.
If you can buy First back then do so. If not get the for the added attack speed which will help you proc Silver Bolts

Phantom Dancer/Shiv
In most cases you'll want to get . If your team comp doesn't have great wave clear get

Armor Pen or Damage
At this point your enemy is starting to have some armor items and you'll be increasing your damage by getting . However if you are far ahead and/or the enemy isn't stacking armor, go

Defensive
Typically I go for the MR, the active, and the bonus damage. It helps me to break a pesky Ult or like an Ult. The list goes on but you get the point.
Now if i'm up against a fed , , or like a I will get to stop their 100-0 Bursts. I included Teemo because his blind is hard to deal with as an adc, especially an auto attack based one. As before the list goes on but those were a few to name as an example.

Early Game
You'll want to focus on your farming so you can build up and get to the mid game. Keeping an eye on your minions health and predicting the enemy ad's cs attempt can land you a quick Tumble poke. Another nice way to poke would be to Auto once Tumble in then Condemn to proc the Silver Bolts.
Melee supports will try and execute minions if they have . You can take this opportunity to get some free poke onto them. Just be careful if you attempt this on a . Also keep an eye out for angles to hit your opponent against a wall with Condemn.

Mid Game
Now you can start fighting with confidence. As always keep your eyes peeled for nice Condemn opportunities. You can take out a pesky split pusher or do some split pushing of your own as long as you are warding correctly. A nice trick I like to do if someone is coming to deal with my split push and I know a fight is about to happen. I'll ward the brush i'm in and wait for them to get close. Just as they almost get into the brush I Final Hour and Condemn them into the wall/brush I just came out of but keeping vision of them since I have a ward there.

Late Game
In team fights you really want to try and keep constant damage going out. So try and take out the high priority targets if you can, but if you are being zoned you can dish out the damage to said threat as well while maintaining good/safe positioning. If the enemy has established you as a high threat, wait out the cooldowns before hard engaging in the team fight.
For example: If the enemy burns his ult, you are now able engage more freely then if he has it still up.

I hope you learned something and will be able to get as much enjoyment out of playing as I have.
Leave any criticism in the comments to help me improve as this is my first guide.
If you liked this guide. You can follow my new Youtube Channel and watch my Stream as I will continue to help players improve.