Hello, my name is Vladislav. This guide has been reworked since the first publish. I hope my readers enjoy it, and that it proves helpful for them.

Vayne is an incredibly strong anti-tank carry. She is weak in early-game, but starts showing her true strength in mid-late game.

This build for Vayne is made by how i play her, but if it doesn't suit your play style, you can change items and runes.

Cons :
1. Weak in early game
2. Very Squishy champion
3. Zero skill for jungling
4. Short range (550)
5. All of Vayne's damage is single target

Pros :
1. Very strong mid-late game
2. Great chasing and escaping tools.
3. Ranged champion
4. Pretty high damage and burst
5. Sometimes stun
6. Her damage is all single target

For runes, i use Greater Mark of Attack Speed, since Vayne needs those Silver Bolts procs.
Greater Seal of Health - some survivability comes in handy in early game.
Since Vayne has no mana issues whatsoever, i take Greater Glyph of Scaling Cooldown Reduction for more frequent use of her Final Hour and Condemn in mid-late game.
I take 1 Greater Quintessence of Health for more survivability in early game and 2 Greater Quintessence of Attack Damage for more harass in early game.
However, if you don't like these runes, you can choose other runes. Remember, this is just a guide, to guide you.

And with the new mastery trees Vayne becomes even stronger.
My mastery trees are 16/0/14.
I spend 16 points in offense, focusing on Alacrity for attack speed, Weapon Expertise for better synergy with Last Whisper and Vampirism for better synergy with my starting items.
I spend 14 points with utility, mainly focusing on Wealth , for more starting gold which is very important for my build, and Good Hands for the lesser time spend dead.

The items order can be freely changed, depending on your opponents. I start with 515 gold because of the new mastery trees. At the start of a game i get a Doran's Blade and a Health Potion . This allows more aggressiveness and harass, while staying in lane in early game.
After that i usually start gathering for a second Doran's Blade , then a Boots , a third Doran's Blade and then upgrade my boots into Berserker's Greaves .
By the time you have these items, you should already be in mid game, meaning you can start looking for kills. Vayne's ult provides damage, yes, but you would want even more, because Silver Bolts are weak in early-mid game.
After that, the item order is custom, depending on your opponents. Let me explain it to you. So, basically, for different opponents you will need different items.

If you are against a mage with CC, then buy a Banshee's Veil , which is extremely helpful for example against LeBlanc's chain attacks, or Veigar's Event Horizon.

If you are up against tanks like Rammus or Amumu, you will need to take Last Whisper and Black Cleaver , for armor penetration.

When fighting someone with life steal, spell vamp. , or any kind of self healing, buy an Executioner's Calling. Examples are Sona, Warwick, Xin Zhao.

Against other auto attack characters, buy a Thornmail Note - i advise champions like Vayne - don't buy this item. You are too squishy to take enough punishment for the item to be worth the gold spend.

Against stealth champions - Teemo, Twitch, Evelynn, etc. - buy an Oracle's Elixir .

Against characters with dodge - Jax - buy a Sword of the Divine.

Pick your ult - Final Hour - whenever possible ( levels 6, 12 and 18 )
When starting a game, the first ability pick is q - Tumble - since Silver Bolts is a weak ability in early game, and you won't need Condemn right at the start of a game.

At level 2 take E - Condemn , which is very helpful when you are being chased by a melee, or if you want to pin someone to a wall, or help your teammates, etc. .

Then at levels 3 and 4, i pick Tumble and W - Silver Bolts , which is a passive ability,. Level 1 of Silver Bolts is enough for early-mid game, and it helps you kill minions faster.

At levels 5 and 6 i take Tumble and Final Hour.

By level 9 i max Tumble. Then i max Silver Bolts , and at last Condemn. Since Condemn doesn't provide much damage, rank 1 is enough for when you are being chased, or you have a team fight in the jungles, and also in some other rare situations.

For summoner spells i choose Flash and Exhaust. They are very helpful and i almost don't use Ghost. I can do pretty good without it. Feel free to change them if you don't like my choices.

So, as i said, i take Flash , which is a great escape/chase tool. It has saved me from ganks, or getting killed a lot of times in early game. It also serves great in chasing opponents in the jungles.
I take Exhaust , which is very helpful against other auto attack champions. For example, Master Yi is dependent on his basic attacks. It also has a lot of other uses. Using it on an enemy champion in early game when he gets attacked by tower is going to either kill him or force him to use his escape mechanisms.

When in team fights, wait for the others to initiate, and stand behind your allies or the enemies will just rip you, and no matter how feed, or strong and good you are, you will be useless to your team dead.
Once the fight commences, start attacking. If you are being focused, use Final Hour , go in stealth with Tumble and kill their carries/important targets, or back up behind your allies while harassing the enemies if you can. Use bushes/good positioning and if you know your enemies, you can easily escape from abilities like Nidalee's Javelin Toss / Takedown , or aoe dmg abilities - Brand , Veigar , Malzahar - Tumble is Vayne's most important and unique ability, which can serve as a manual dodge to a lot of other champions abilities.
One thing to remember, if there is a tank with 3-7k health, Vayne's Silver Bolts will rip them, so if you have a good attack speed, feel free to attack the enemy's tanks as well. You must pay attention and try not to attack tanks with Thornmail or when their shield abilities like Rammus's Defensive Ball Curl are active, unless you have lifesteal. First kill the tank's teammates, then focus on him when he is left alone.

Unfortunately, until Vayne gets to level 6, she is not good at ganking. However, when she gets her ult, and 1,2 items, she becomes deadly. Ganking with Vayne is simple. Tell your friend to play defensively, and let the enemy to push into lane. When the enemy pushes to the tower, attack him from bushes, and if you are good at positioning, ping him to the wall/tower with Condemn and then kill him with your teammate.

With the changes to mastery trees, it provides a better survivability and aggressiveness in early game, while in mid-late game it devastates enemies. I've had a lot of games with triple or quadra kills(i perfectly know that doesn't determine player's skill), I've managed to beat in 2v1 fights quite a few times. One thing to remember when playing with Vayne is :
If you want to win, make sure you do the first strike, since Vayne is very squishy champion and she can't handle much damage. Some players think Vayne is not good in team fights, but they are wrong, as she can burst even tanks pretty fast, due to the items armor penetration and her Silver Bolts true damage.

For those who don't know the League of Legends abbreviations, let me explain it to you.
AD - Attack Damage
AP - Ability Power
AS - Attack Speed
AA - Auto Attack
CC - Crowd Control
OP - This can mean two things. The first is Original Poster ( the creator of a thread/quoted post) . The second is Overpowered, for champions who are by some unfair way stronger that other champions.
LoL - League of Legends.
Jungler - a player who kills mobs and ganks players in the jungle.
In-game abbreviations are :
ss - this is short of MISSING - missing from lane. For example, when someone says ss top - that means the enemy player there is missing, and is probably going to gank someone.
MIA - also meaning MISSING from lane. The same thing as ss.
re - this is short of RETURN, meaning the enemy player has returned to his lane. Example - re top.
Inc - Incoming. When an enemy player is coming for a gank and other situations.
Fed/feeded - this means the enemy player has a lot of good items in his pocket.
Noob - i don't think i have to explain this one.
Care - careful.
Gank - when 2 or more players are attacking 1 player.
League of Legends ( LoL ) item abbreviations :
GA = Guardian Angel
FoN = Force of Nature
SotD = Sword of the Divine
RoA = Rod of Ages
BV = Banshee's Veil
IE = Infinity Edge