This is my first time writing a guide, so hopefully it'll help you and I will get some good feedback!
It is a Work In Progress, but I've got the build and just have to write it out, please be patient =)
Vayne is an awesome carry. She's relative to Ashe, but way more bursty and has the ability to kite, possibly even better than Ashe because she can roll around every second and push enemies into allies depending on the fight.
Pros / Cons
Insane ability to carry a team.
Able to focus down almost anyone 1v1.
Kiting ability is insane with tumble and slows from frozen mallet.
Able to turn the game around at any given moment with her damage output.
Extremely vunerable to stuns.
Requires positioning to stay alive/activate skills.
Needs teamwork to really thrive late game.
Not really any escape skills besides kiting with slows and your summoner spells.
You want to go straight down the offensive tree getting mostly damage points and such!
Down the Utility tree to Utility master, ignoring expanded mind, but grabbing Utility master because having red buffs and frozen mallet on Vayne is a double whammy since you get a DoT to accompany the slow.
Ghost - Used to chase and run away ( your passive doesn't help you run :( ) Good survival tool and gank tool just in case they are 1 step ahead of you!
Flash - Used to chase or Flash past walls ( your Tumble doesn't go through walls ) Excellent when you need to jump in with an ult and jump out leaving with 2-3 kills and your life!
Exhaust - It's possible to use this, but it doesn't seem to be much help as you can already kite those physical fighters and it only reduces magic users damage by 35% and slows them which, if they are running already, you've proc'd frozen mallet on them.
Cleanse - Could have its uses as she has no escape mechanism. Basically, if you are CC on Vayne, you are dead and messed up!
Teleport - Possible, though Vayne should always be in teamfights ,no exception. She is the team's carry after all!
Do not touch please =/(Sad Vayne):
Clairvoyance- You are not a support character and you have no escape mechanism. You can't afford vision over survival!
Clarity-You never have mana problems, so why?
Fortify-You are not the tank, you need to focus on CC with Exhaust or Ghost after a weak enemy.
Heal- If you try to heal, you're most likely dead anyway.
Ignite- Vayne doesn't leave her prey alive. She doesn't need Ignite to impale her prey!
Rally- Almost useless spell that can be destroyed almost instantly, though it's a portable ward, I guess?
Revive- Are you a feeder? Vayne should be the one doing the killing!
Smite-Jungle Vayne? Could be possible, but isn't it better to shut down a lane so you're lvl 5 and they are lvl 1 instead of a leveled playing field?
Passive - Night Hunter, This, with boots, allows you to harass almost anyone in early laning.
Q - Tumble , This skill is close to being your bread and butter and I say close cause you proc Silver bullets more than you can spam Tumble. This is probably one of the skills you'll be using mostly to damage an opponent to weaken him for the kill or chase down someone with.
W - Silver Bullets, This is truly your bread and butter because if you can max this right away after tumble, every 3 hits you proc about 8% of life away from your opponent. You may think 8% for 3 hits "Wow that's not a lot", but Vayne is played on weakening her prey and impaling them upon the wall. (8% + tumble proc(sheen) + AD)
E - Condemn, This skill is nice to have lvl 1, but no further than that. The cooldown is way too long and the damage is too little, requiring you to build nothing but AD to do insane damage with it and have a wall with your opponent ( any wise opponent won't stand next to a wall, it's up to you to put them next to it).
R - Final hour, This is your ult. You'll love and cherish it and no, it doesn't suck as this ult nearly gives you all ability to chase down anyone including a Rammus and almost doubles your dmg by giving you a bonus 75 attack damage. You will have to activate this when you enter the fight and position in that first 1.5 second to stun their carry and proceed to annihilate the team within your ult time limit.
The main goal of this build is to max out your Tumble (for those fast 1.5 second double dmg moments) and silver bullets to drop anyone you lane against.
Sheen - Awesome for Vayne. It means everytime you cast Tumble, you not only get the bonus damage from Tumble, but you get double dmg on your base AD!
Berserker Greaves - Overall decent boots for Vayne. They help her pump out silver bullets and they also increase her movement speed to lvl 2
Frozen Mallet - Overall great for Vayne. It gives her livability and also needed to keep those physical brutes away and on the rope!
Infinity Edge - You'll end up building this, which add crits to your Tumble! Also 250% dmg from the Tumble, giving you a whooping 80 atk damage to Vayne =) It's like her ult on, 100% of the time!
Phantom dancer - This is mostly used to proc her silver bullets and increase the crit rate while giving her a slight better survival due to the small increase in your already powerful chase!
Guardian Angel - Who doesn't want a Guardian Angel who can bring you back to life to stay in the fight? After all, you're the team carry, we wouldn't want you to die now, would we?
Trinity Edge - This'll be the last item you can make to max your slots. It's really only useful for increasing your already 60% crit and all of your overall stats, adding everything from survival to damage, not to mention making the sheen do 150% dmg now!
At this point, the game is heavily reliant on you, which is why you need to stay alive!
If you die, it could spell doom for your team. At this point, you will most likely want to go into situational items instead of running into Phantom Dancer, unless the game is clearly in your favor!
Last Whisper - Consider building this when the team built nothing but armor!
Banshee Veil - Crowd control a problem? This might help?
Guardian Angel - Need a second life? Here you go.
At this point, it's up to your team to coordinate. Your goal is to let your team initiate ult in and Tumble aim for the carry and pin them on the wall. This makes it so your team can easily focus without a cow blocking the carry!
If the game just won't end you finish your Item Set!
If your team protects you, which they have to, Vayne's late game relies on the team heavily! You should win. Good luck!
I will be making changes as I see it fit, possibly making this build better. I hope I can make it awesome!
-1.36.14 Due to the small nerf to vayne her early game is changed!