Hello everyone. This is my first build on mobafire, and I'm going to tell you about my way to play Vayne.
Vayne is an amazing champion in many ways. She looks cool, her moves are stylish, she has some decent abilities, and she's also very fun to play.
I'm not saying that this is the one and the only way to play her, this is just what i think of her play-style. I will be updating this guide to keep it up-to-date, and to improve it.
Any feedback is really appreciated, but please, don't downvote before you try it out!
Also, I'm sorry for any grammar mistakes you will find in this guide, since English is not my native language.

The world is not always as civilized as people might think. There are still those who would follow the blackest paths of magic and become corrupted by the darker powers that flow through Runeterra. Shauna Vayne knows this fact well. As a young privileged girl in the heart of Demacia's elite, her father tried to convince her of the constabulary's ever-vigilant eye. Young and naive, she truly believed that her world was one of perfect safety, until one night, when a twisted witch took interest in her father. The malevolent woman overcame her father's conciliar guard, then tortured her family before murdering them. The young Shauna escaped only by hiding herself and then fleeing once the hag had departed, plagued by the screams of her loved ones as she ran. A burning hatred was born in her that day, one that could never be denied.

Vayne was able to take care of herself using her father's money, and she began to train as soon as an instructor would have her as a student. By the time she was a fully grown woman, she had become a grim warrior. However, the fields of battle were not to be her home. Demacia needed a protector, one who hunted those lost to the darkness. Shauna used her family's contacts to become the first Night Hunter, and now her prowess is the stuff of legends. It is said that those who practice the black arts quake when they hear that the Night Hunter is on the prowl. Despite her crusade, Shauna has looked at the League of Legends in horror. There are champions who have clearly lost themselves to the blackest of magics, and who have been embraced within the League even though they should be put down for the safety of all. The time has come for the Night Hunter to execute her secret mission - to purge the League of Legends.

Not all shadows are to be feared. At least, if Vayne has her way.

Pros:

Great damage output
Passive deals a lot of true damage
Not very mana-hungry
Not a fully auto-attack champion (that's a big '+' for me)
No one can run away from her ultimate
Has some sort of natural escape mechanics (condemn, ultimate+tumble for stealth)
Looks very cool
Fun to play

Cons:

Squishy
Vulnerable to CC
Condemn can stun, but is not reliable
It's hard to position yourself well in team-fights
Often targeted first
People will say you play an OP champion

Vayne ruthlessly hunts evil-doers. She gains bonus Movement Speed when moving toward nearby enemy champions.

This is your passive. It gives you 40 movement speed when you are running toward an enemy champion. This is an awesome passive for killing fleeing foes. However, it only works if you can actually see the champion, so if he moves into a bush, you will lose your bonus.
To clarify: lvl 1 boots give 50 movement speed; lvl 2 boots give 70 speed; lvl 3 boots give 90; and lvl 5 boots give 125 speed.

---

Vayne tumbles, maneuvering to carefully place her next shot. She rolls toward the cursor and her next attack deals bonus damage.
This makes you move on a short distance. The distance you move at is really short, shorter then the distance of any other skills of such a kind. Notably, you can not use it to cross any impassable terrain on the map (such as cliffs or trees), because the travel distance is just not long enough.
Tumble also resets your auto-attack timer, which means that if you use it right after a normal attack, you will be able to auto-attack again immediately.
Please note, that when you are under the effect of your ultimate, using Tumble will put you on stealth for 1.5 seconds. While this is not long, it can be really helpful in ganks, and also used as an escape tool. If you see a gank which will definitely kill you, do not hesitate to use your ultimate+tumble to run away.
Don't forget that this skill moves Vayne towards the location of your cursor (works like Karthus's Lay Waste), so you don't need to click to use it.

---

Vayne tips her bolts with a rare metal, toxic to evil things. The third consecutive attack or ability against the same target deals a percentage of the target's maximum Health as bonus true damage. (Max damage vs. Monsters is capped)

This is an amazing skill. Not only it adds a flat 70 damage to your 3rd attack on the same target at skill lvl 5, but it also deals 8% of target's maximum health as true damage. That really makes a great burst and deals great amounts of damage even to high-armored tanks. Obviously, you will want to make this passive work as many times as it is possible, so items with attack speed suit Vayne well.

---

Vayne draws a heavy crossbow from her back, and fires a huge bolt at her target, dealing damage and knocking them back. If they collide with terrain, they are impaled, dealing bonus damage and stunning them.
This skill is great for both offense and defense. Offensively, you can use it to stun the target if your positioning is good, or to knock the enemy away from his tower/teammates. However, it is sometimes hard to take a good position and use this skill with full efficiency.
Defensively, it is most obviously used to knock enemies back from you.
You should also note that it can be used to interrupt any channeling spells, such as ultimates of Nunu & Willump, Katarina, Karthus, Miss Fortune, Janna, or any other skill that takes time to cast. This can greatly help your team in team fights, so use it wisely.

---

Readying herself for an epic confrontation, Vayne gains increased Attack Damage, stealth during Tumble, and quadruple the bonus Movement Speed from Night Hunter.

Her ultimate is really awesome. While the only stats that scale with the skill lvl are bonus attack damage and the duration of the ultimate (8/10/12 seconds), it offers you unique opportunities to gank enemies. It's not even about the 1.5 seconds of invisibility after your q, it's about the speed increase. Your passive bonus gets a 4x increase, which means you will get 160 bonus movement speed.
To make sure you understand. Ghost adds 27% of movement speed, so a target with Boots of Swiftness that uses Ghost will have a total of 400+400*0.27=508 movement speed, and you will have 560. Pretty amazing, isn't it? That's why i say: no one can run away from Vayne.

For now, i stick with Armor penetration marks; Attack speed seals and glyphs (attack speed is good for your Silver Bolts, but you do not get a lot of it from the items); and Health per level quintessences for better survivability late game.

At the moment, i chose 21-0-9 for the masteries. I do not take Archaic Knowledge since none of your abilities deal spell damage.
I also don't take Lethality because i do not really rely on critical strikes, and put some points into Offensive Mastery instead for easier minion killing. However, you can put the points in Lethality if you want, since we are getting Infinity Edge anyway.
I also take Alacrity because more attack speed gives me more damage from Silver Bolts.

As for the utility tree, i take Awareness for faster leveling, and put the last point in greed to get some free gold.

Let's talk about summoner spells.
Personally, i prefer to play with ignite and flash, but let's see what each of them can give us. Flash is one of my favorite summoner spells. It can used as an offense or defense ability, and it can also be your panic button. A good usage of Flash on Vayne is when you flash into a position, where the enemy champion is in between you and a wall. This will allow you to stun his with your E, and get a couple of free shots.
What can I say... It is a perfect tool to finish off a running enemy. It also helps you to cut through tanky enemies since the damage is armor-ignoring. And last, but not least, it haleves enemy heals, so it becomes irreplaceable when you face healing enemies, such as Dr. Mundo, Soraka, Nidalee, Taric, and so on.
As any other DPS champion, you are weak against any crowd control. You are very squishy, and any stun/suppress/air knock will get you killed. So cleanse might be useful to save your life.
Teleport is good for map control, saving towers, and ganking after teleporting into bush. Take it if you want it.

---

Vayne does NOT need it as an offensive spell, since she has more then enough to catch running targets. However, you may take it as a defensive skill to reduce enemy damage and to avoid ganks. I don't like it personally.
Same story, you do not need it to chase enemies, but you may use it as an escape tool, or if you need to rush across the map.

---

Revive: Just... no.
Heal: Heal might seem useful in early game, but it does not help in the late game at all.
Smite: You are not going to jungle, are you?
Fortify, Clairvoyance: A support should take these, not you.
Clarity: If you are having mana issues, you are playing wrong, sorry.

---

Tumble should be your main damage source, especially in the beginning of the game. It works pretty much like sheen, increasing your next attack's damage based on your total attack damage. That means you don't need a lot of AD to hit hard: since the mana cost is very low, you can use this ability to either harass your opponent and to last-shoot minions.
Also, don't forget that this skill resets auto-attack timer, so if used right after a normal attack, it will allow you to make an instant second hit.

At lvl 2 you get your first rank in Silver Bolts, which will be your second harass ability. Now you can try to harass your opponent not only by hitting him once after using your Q, but trying to shoot 3 bullets on him, to make the passive work. That will deal alot of damage, and, if done properly, will make the enemy champion leave his lane to heal very soon. Also this helps to deny him some experience.

At lvl 3 you should get your first (and only) rank at Condemn. You should max this skill last for a couple of reasons. First, it does not really deal that much damage, and the scaling is poor too. Second, it has a very long cooldown. One rank should be enough for its main purpose: to knock people away, and to throw them on walls.

I always start off with Boots and 3 Healing potion's.
The reasons are simple: if you do not take boots, and your lane opponent does take them, your passive becomes useless since he still runs faster. Also, you are really squishy at low levels, so those potions may be really handy.
After you have about 1300 gold, you should head back, and buy yourself a Sheen and, if needed, one or two healing pots.
Sheen should really be your first item, because it fits your Tumble so well!
Not only this item (and your tumble) does increase the base damage of your next attack, they also have the same cooldown at higher levels of Tumble, which means you will have sheen proc every time you are going to use tumble.
When you have Sheen, you will start to deal significantly more damage, and can start being more aggressive.

Your next item depends on how good are you doing. If you have a kill or two, then go ahead and grab a B.F. Sword before the catalyst. The damage it gives will be more then enough until late game, since your base damage is greatly increased by sheen and tumble.

If you are not doing well, getting harrased, having hp troubles and so on, go for the Catalyst before the BF sword. It will restore some of your health and mana after leveling up and help you stay on the lane longer.

After those, your next step is to make Banshee's veil.
Vayne is kinda weak if she can't keep her distance. Champions like Xin Zhao, Jax, Blitzcrank, Rammus (with his taunt and Powerball), Akali and so on are dangerous for you because of their burst damage. You are also weak agains AP champions that have a cc, including Kassadin (can't catch him either), Nunu & Willump (his snowball hurts alot), Anivia (though you can dodge her Q spell with tumble) and so on. Banshee's Veil's passive helps greatly against them. It also gives you some health, which is always nice to have.

After your Banshee's Veil, you should finish your Trinity Force.
Start with getting a Phage first, because of the slow chance, and because it gives additional hp.

I consider the items that you are getting after Trinity Force to be situational, so I will talk about them later, in my situational items section.

You should not always stick with the item order that is listed above. Every game is different, with different enemies and different threats. Lets talk about some item possibilities.

First of all, the boots. I usually take Boots of Swiftness to get as much movement speed as possible, which is both helpful for chasing enemies, and (which is more important) for getting away.
However, if you would like some attack speed, you should go for Berserker's Greaves. In that case i would advise you to build boots before BF sword, since they don't cost much and will give you more damage from Silver Bolts.
If i happen to lane versus either a high-damage mage champion, a champion with a CC, or both (like Le Blanc), you can consider buying Mercury's Treads. In this case you should go Boots-> Null magic Mantle-> Mercury's Treads, and once again, build them before the BF Sword.
All other boots types are kinda bad for you, so i don't take them into account.

Items for different opponent team setups.
If the enemy team has 2 or more high-dps champions, and/or if you lane an AD champion like Ashe and are having problems with her, consider buying a Chain Vest which you should build into Atma's Impaler. With my build you will have around 3k hp in the lategame, so Atma's Impaler will give you decent attack bonus as well as a crit chance bonus.
There are two other items that can aid your killing ability, and at the same time give you AD protection: Madred's Bloodrazor aka "The Paw" and Wriggle's Lantern aka "The Lamp".
While Madred's itself is a good item, I would not recommend you building it first. Your Silver Bolts will deal much more damage then this item. Not to mention, it costs almost 4k gold.
The lamp is a better choice. It offers lifesteal, as well as a chance to deal massive damage to a minion. Its active ability is useful for map control too, especially if yo are laning.
Finally, you can just buy Madred's Razors without upgrading them to anything, and sell them later in the game if you will no longer need them.
Hexdrinker is a great item for you, if you are facing 2 or more high-burst AP champions. This will not only give you some extra Magic Resist, but also will give some attack damage, and a shield which is particularly useful in 1on1 fights and for running away. Also, since you are getting Banshee's Veil anyway, you will have some nice magic resist which will be useful late-game, and/or if enemy AP carry gets fed.
Wit's End is another good anti-mage item, especially after the last patch. However, i find Hexdriner to be more useful because of it's passive, and it also costs less.
Atma's Impaler-> Bloodthirster
This is pretty straightforward. Atma's impaler gives you about 58 attack damage with this build, as well *** giving you more survivability with it's armor bonus. Bloodthirster is a good finishing item, however i would not recommend you getting it as one of your first items. It loses it's stacks after death, so the damage amount is not constant and not very reliable.
Infinity edge will give you a better damage outpus, and thus it should be preferred.
Black Cleaver-> Last Whisper
If you see that 2 or more enemy are getting tanky items, you can actually go for Black Cleaver earlier, getting it from that first BF Sword that you buy.
In the early/mid game, Black Cleaver is better then Last Whisper. Let's do the math.
Last Whisper reduces enemy armor by 40%, and Black Cleaver stacks armor debuff 3 times, leading to a total reduction of 45. That means your target should have at least 112.5 armor for Last Whisper to be as effective as the cleaver (112.5*0.40=45). Also don't forget that The Black Cleaver can reduce enemy armor below zero.
Of course, later in the game, Last whisper's armor reduction is superior to Black Cleaver's reduction.
CC is your killer. With the introduction of new items, you dont need to buy Mercury's Treads to get CC reduction anymore. However, those boots are actually good for us, as I have mentioned earlier.
Here i would like to talk about an amazing item which is often overlooked: Quicksilver Sash.
This item is amazing. It gives you a ton of magic resist, and it's active removes any debuffs from your character. Literally any: it is capable of removing Mordekaiser's ultimate, Ignite, an any other debuff you can think off.
If you face a heavy CC team, you should think about buying this item. If you face a CC-heavy AP team, this item is your best friend.

More detailed section coming soon!

First of all, Vayne is extremely good with harassing. She can start doing it on lvl1 with her Tumble. On level 2 you get Silver Bolts and can harass even more. And later in the game, your ability to make people stay away from you and your minions becomes even better.

Vayne is a great mid. However, she is as good at a duo-lane, or solo top lane if it's 1vs1.
Most of the champions that you will face will be squishy, and you can easily dominate the lane by constantly harassing them, and denying their exp and gold.
However, you should focus on last-hitting too, because the items you want to get are really expensive and you will need to get as much gold as possible.
If you have ignite, you can actually get your first kill at lvl3. If you manage to stun the enemy with Condemn, the kill becomes an easy goal for you.
If you understand that you will not be able to stun him, then save your Condemn for the last hit, when you will be in tower range. At this stage it doesn't matter that you will knock the enemy champion closer to his own turret. The condemn damage is more important, if you think he'll die from ignite.

When you get lvl6, and go back to the base to get your Sheen, you can try to gank one of the lanes, because at this stage your damage is really impressive.

In team fights, pick a target to use Condemn at. It can be a champion with a taunt such as Rammus, a champion with a channeling skill suck as Katarina, or a melee dps such as Garen. In each of this cases, you can win your team a couple of seconds by knocking your target out of battle (preferably to the wall, of course!).

Don't forget that Vayne is very squishy, even with the hp from Trinity Force and Banshee's Veil, you also don't have any lifesteal with this build. The main threat for you are burst damage champions with CC abilities: Xin Zhao, Akali, Irelia and so on. While you can use codnemed to knock them away once, it is sometimes not enough, and if you get knocked up/stunned, you are as good as dead.

Here's my thoughts on playing Vayne, the Night Hunter.
This guide is still incomplete, and I will be updating it soon, adding a detailed item section, a more detailed gameplay section, and some pictures.
Please leave your comments, constructive criticism is always welcomed!
Thanks for reading.