Hello I am Aeonidas! I've been playing Vayne since ~mid Season 2 and although I may not be some sort of god, I do know quite a bit about this champion. I decided to take some time and make this guide to help some of the newer Vayne players out, but since it's my first guide it might not be too good!

Items
Firstly, items. Vayne is typically built more of an assassin/dueler style than ADC because her dueling potential is insane. Blade of The Ruined King is great for shredding tanks, since it does % HP damage and being paired with Silver Bolts is tremendous amounts of damage. Pretty much all you need on Vayne is lots of attack speed to make kiting easier. Although, if you just build full attack speed you won't be as relevant late game but the fix to that is simply building an Infinity Edge. When positioned correctly, using this build does a lot of damage. Also, build Guardian Angel because the enemy team will focus you HARD.

Masties
Pretty much standard AD masteries, and 'Dangerous Game' is extremely strong for dueling which is all Vayne is about.

Runes
Life Steal quints for survivability in lane (paired with Doran's Blade the sustain you get is very good).
1 Critical Strike mark because even though it's a very small chance (0.93%), just one crit can win you a duel.
Everything else is pretty standard, I chose flat armor/magic resist runes over scaling because I feel that they help a lot with getting through Vayne's early game.

How to play Vayne
With Vayne, you need to be really good at attack moving to play her at her fullest potential. If you don't know what attack moving is, it's when you press A and click to attack whatever is nearest to your cursor/ whatever you have your cursor on. For me I find it really tedious to click after pressing A, so I changed it to pressing A only which can be done through options.
Vayne's laning phase is actually not as bad as people may think, I would even go as far as to say it is one of the stronger phases in ADCs. Although she lacks burst/poke, it is very easy to harass with Vayne. Two stacks on Silver Bolts, walk back a bit, then Q backwards to pop Silver Bolts again (in lower ELOs people don't know how to react to that so it should be pretty easy :p). Keep in mind though, Vayne's attack range is only 525 meaning champions with higher range can easily harrass her (this is why people perceive Vayne's laning as weak). Don't worry though since as soon as you get Ruined King you can out duel almost anyone (unless they're fed, of course).
Now for the most important part, team fight positioning. With Vayne, it's really easy to outplay the opponent but it's also very easy to outplay yourself. Just stay at the back line, attack moving and hitting who ever is closest to you. One of the things I learned was that when you're invisible, attack moving doesn't work so you have to use right clicks. This is extremely important because if you attack move while invisible you will simply just walk up to the enemy and get insta-killed as soon as it runs out. During a team fight, make sure to keep moving so you can dodge skillshots/cc and if you're getting focused don't hesitate to flash or heal but don't overdo it and use both flash and heal at the same time. When the front line that's diving you is dead, or when you see an open path to the enemy carries, skirt around the team fight and focus them down. And although she is more of a big play making champ, working with your team is also very important as Vayne.
The last thing I wanted to talk about is dueling/split pushing. In the later stages of the game, dueling someone can either win you the game, or lose you the game. Vayne is notorious for being an extremely high damage dealer in the late game but don't forget that she can also get one shotted very easily. When dueling someone, make sure that you keep moving around to avoid as much damage as you can (skillshots, cc, etc). This is what your average late game duel should look like: Play Video
Notice how I kept moving around in the duration of the fight, and used my attack move to get as many auto-attacks off as I could.

Play Video
-This is a pretty neat trick, although it doesn't really serve any real purpose you never know when it might come in handy. To do this, simply Condemn the enemy and flash as the animation goes off to get the stun.
-In the early game, any auto attack resets you get are crucial since you have low attack speed. Go to the corner of the dragon pit with the sign, and auto, and then Q backwards into the wall to get an auto attack reset.
-Another trick I find useful is re-engaging the enemy when you make it appear like you're running away. For example, pretend like there are 2 people chasing you (ADC and support) and you're alone. If you have at least Ruined King and heal you can probably turn around and kill them both (or one, preferably ADC though). What you do is pretend like you're running, and then as soon as you see an opportunity to condemn you instantly use R and Q to one side to get invisibility and then condemn the carry. Then pretty much all you do is auto attack away and try to avoid the support's CC by constantly moving, and don't forget to use Ruined King or heal if you're taking a lot of damage.


Tips
-My playstyle with Vayne is generally just farming/harassing in lane unless you see a good opportunity to go in. Right as you hit level 6 you get huge kill potential due to the ultimate.
-Don't push your lane too far ahead before getting Ruined King as it will be extremely easy for the enemy to 3v2 your lane.
-When you get items, don't be too afraid to duel the enemy. Make sure to keep pressing TAB and checking what items they have before dueling them because well, even Vayne can get out dueled.
-Just farm up, duel whenever you can, and you should be set!

NOTE
Condemn is NOT a harassing tool. Never spam it in lane, unless your jungler comes to gank and you see an opportunity to get the stun off.

Thank you for reading this guide, I hope it was useful! Since this is my first guide I would greatly appreciate any feedback you guys have. Happy climbing!