Vayne... that it sounds like vain is no coincidence. Fighting against her is, in most cases, totally in vain.
Vayne is mostly a normal DPS-Champion. She posses great harassment and chasing abilities and she is a formidable ganker, thanks to her ultimate.
If she is played with the right items and the right tactic she becomes a great champion throughout the whole game.

There are plenty of posibilities for runes.
For marks I tend to use Greater Mark of Critical Chance just for the feeling of "DAMAAAAGE!" but the Greater Mark of Desolation is working quite well, too. Both of them provide some early-game damage, which is necassary for Vayne.
With seals I tend to use Greater Seal of Replenishment because if you are forced to use Tumble for harrassing well in early game, your mana will be gone very fast. However if you are sure, your mana will last, use Greater Seal of Evasion for supporting your dodge mastery.
For Glyphs I use Greater Glyph of Attack Speed simply because I think that even the tiniest bit of attack speed will work for Silver Bolts. I suppose you could use Greater Glyph of Magic Penetration, too, to increase her overall ability damage, but I don't recommend it.
Finally, for Quintessences I go for the Crit chance, with Greater Quintessence of Critical Chance, for the same reason as before. You can also choose to stick with Armor pen. and use Greater Quintessence of Desolation or go for the simple Greater Quintessence of Health. All three tend to provide satisfactioning results.

I tend to use simple 21/9/0 with improved Exhaust and dodge. The additional armor is in most cases vital for early-game success, beacause against popular believes, Vayne is squishy, especially without Doran's Blade as starting item.

So, the important part, items. Right from the beginning, most guides suggest Trinity Force, but I don't. I know, the passive may be nice and the overall stats my be suitable for Vayne, but my head keeps repeating: Ability power is useless... So I don't use it. Plus I think Trinity Force is far too expensive. But that's just my opinion, if you don't agree, use another guide, because you can't add it somewhere here.
But lets get to my build. I start with Regrowth Pendant and one Health Potion. That gives her a good health regeneration and allows you to stay on lane quite some time.
Then rush to B. F. Sword and if possible buy Boots right with it. That'll cost you 2000 Gold, but with a few kills, you should be able to afford it. The B. F. Sword will increase your damage output greatly, suprising your opponents. The Boots, linked with Night Hunter will allow you to chase enemies down.
Now you should grab Black Cleaver for the additional attack speed and armor penetration. Then get Boots of Swiftness, as mobility is one of the keywords for Vayne.
At this point of the game, your damage output should be good enough for mid-game. However you will notice, you'll die too often, especially with the enemy team focusing you.
So our next investment is Warmog's Armor. I can nearly see the WTF on your face right now, but believe me when I say: This. Is. Great. It will expand your life to about 2.5k, depending on your level. That will make you super hard to kill in 1vs1 or even 2vs1. No combine this durability with the damage provided by Black Cleaver and you should be able to kill everyone.
But one important thing: Don't you ever dare to think of yourself as off-tank. Yeah, you got health. But that's it. A friend of mine made that mistake, and believe, that didn't end well.
Warmog's Armor is for Durability only! And ONLY!
After getting it, you can get back to damage Items, either Infinity Edge or Bloodthirster. I recommend the Edge first, because lifesteel with Vayne is different. The triggering shot from Silver Bolts doesn't count as normal attack, so it doesn't give you any health. In addition, the health regeneration from Warmog's Armor should be enough.
Most of the games will end somewhere till that point, but if not, you can get Phantom Dancer or Madred's Bloodrazor.

I am normally starting with one point in Tumble, but depending on your lane partner that may differ. With a lane Partner with CC get Silver Bolts if the damage of your partner is higher than yours, take Condemn. Anyway, use the following two levels to get one point on each ability. Then start maxing Silver Bolts, as this is your main source of damage.
Some might say, maxing Tumble first is more useful, as it deals more damage. But for harassing the Silver Bolts are far more useful, especially against tanky enemies. Plus Tumble was nerfed a little bit.
However, max Tumble second. That will increase the damage and lower the cooldwon. Max Condemn last, as it mainly serves to pin enemies to walls and only gets stronger with higher levels.
Of course, max Final Hour whenever possible.

Lets start with Tumble. Tumble is like Flash. It brings you to a location near your cursor. However, walls do stop it, so be careful not to get stuck at a wall.
Used once, it gives a buff for the next auto attack. The cooldown timer does only start after you used that buff. For escaping with Tumble, use it once, fire back, use it again, or you'll have to wait additional six secinds until you can use it again.
Silver Bolts is as easy as it sounds. Attack a target three times and bonus damage is dealt. If you attack a different target before Silver Bolts is triggered it will be resetted. The triggered shot doesn't count as normal attack, nor as magical attack and therefore isn't affected by spellshields, like Banshee's Veil or Black Shield, but also doesn't give you life steel or spell vampire. You can crit the auto attack that triggers it, but said isn't displayed as such.
Condemn pushs an enemy back, when he hits a wall, he is stunned for 1.5 seconds. That's it. You can use it to save allies, or use it on "I'll jump into that enemy crowd and back"-Champs like LeBlanc to effectivley stun them. You may also use it to shoot enemies out of Jarvan IVs Cataclysm.
Finally Final Hour. It can be used in many ways. The most obvious way is to chase down an enemy with the extra movement speed and attack damage. You should be using it that way most of the times. You can use it in teamfights, too, the extra attack damage hereby being the main point. If you are a bit skilled at escaping, you can use Final Hour for it, too. If the enemy is chasing you, activate it, and tumble back. Because of the stealth the enemy will run straight foward and you will get the movement speed buff for running towards them. Finally you can use it for mid ganks. Wait in the brush until the enemy champion is near your teams tower. Activate Final Hour, Tumble forward and until you'll be visible again, you should be right behind the enemy with no way to escape for him.

Early-Game

In early game, harassment is your main task Tumbleshoot an enemy whenever possible, try to get three shots in a row to trigger Silver Bolts and Condemn them to walls to get easier shots. You should focus the weaker enemy, to actually get a chance to get First Blood. In early-game, don't hesitate to use your ulti to get a kill, as those kills are vital for your ongoing success. Keep in mind, that Vayne is a squishy champion and can be brought down easily by combined attacks of two enemies.
If your lane is doing fine, feel free to gank mid with the tactic mentioned before.

Mid-Game

In mid-game you can go for higher risk, as Warmog's Armor will give you great durability. Don't hesitate to chase down enemies, even with one or two of their allies next to them. Mid-game is your time. With Silver Bolts maxed out, you can bite out big chunks from tanks, and the armor penetration from Black Cleaver is helping quite a lot. Your the antitank. Encounters in the jungle should always be started with Condemning the enemy to the nearest wall. That will give you a time bonus. Overall fights should consist of normal attacking, while using Tumble to stay at midrange. Easily put, Tumble away from Meeles and towards Ranges.

Late-Game

Late-Game consists mostly of teamfights. Your tasks in teamfights are:
1. Dealing damage to enemies while staying out of range
2. Stun enemies whenever possible with Condemn
3. Chase enemies with Final Hour, who are trying to escape
You shouldn't wander around the jungle on your own, but seriously, in late game, no champion should. In late-game, you lack the possibility to escape quickly, as tumble doesn't bring you far away and you are slower than most of the other champs. So make sure you'll stay wiht the team.

Just a short paragraph about Summoner Spells. I'm using Flash and Exhaust, mostly standart. Do I really have to explain why?
Other useful possibilities:
Cleanse: Always helpful to get out of CCs
Heal: If timed right, deadly
Ignite: To get the last health points down.
Other special posibilities:
Ghost: A bit pointless with Tumble and Night Hunter
Clairvoyance: If you can use it, there you go.
Teleport: You can... if you really want to, I suppose you can.
Useless possibilities:
Smite: Your not jungling, so why would you...
Fortify: Your not a taunt tank...
Rally: No...
Revive: NO! Just... no.

So... I hope I could bring some light in the Darkness of Vayne. If you think I've made my jobe good, vote so :)
I know I'm going against main stream without Trinity Force, but I just don't like it. When I'm playing Vayne, all the stuff I mentioned works fine, but that doesn't mean it works with every playstyle. If it doesn't suit you, take a different guide.
Much fun with Vayne!
Chorus