Welcome to my guide.
This guide will focus on pure attack speed and her true damage abiity. Please rate and comment

Pros
+ her true damage can not be resisted
+ nearly no one can escape her
+ her "e" can help counter incoming ganks
+ true dmg + Madred's magical dmg + phisical dmg. Try to counter this!

Cons

- squishy
- if you let some melee dps get close and personal with your "e" on cooldown you have a problem
- easy to shut down
- you need to have a good team which will protect you

Vayne is squishy! My runes and masteries makes every phase of the game easier adding some survival. You can also take flat hp runes to help your early game.

Recurve Bow is my favorite items in case of Vayne. With all other items you can quickly kill everyone. It's a percentage damage. Madred Bloodrazor is a high priority because of passive. Starks Fevor gives you some life steal and Wit's End some magic resistance. Sword of Divine passive works on towers. To boost your AD use your ULTI.

Enemy Jax?? Sword of Divine after Madred's Bloodrazor.

After geting all items your dmg should be as follows:
-3% max hp magic dmg
-42 magic dmg
-3% max hp magic dmg
-42 magic dmg
-3% max hp magic dmg
-8% max hp true dmg
-42 magic dmg
-3% max hp magic dmg
-100 magic dmg
-42 magic dmg
And all of this in only 4 auto-attacks!

Get in, kill, get out. There is no better spells for this. Also ghost + flash are great escape abilities. Your passive + ulti will be enough for chasing enemies.

You can also max "q" first to make easier to get in range. Another way is to max "q" and "w" in same time.

When you fight and you are 50% sure that you will kill enemy with your last attack it is better to use "e" for final blow. If you fight Kog'Maw your killing blow should ALWAYS be "e".

Do not chase Eve or Garen even if you use ghost and ulti. YOu wont catch them.

In early game the best partner for you is any support: Soraka, Sona, Taric, Kayle etc. They allow you to farm minions and heal you if enemies will be aggressive.

In teamfights you should target enemy team carry. You enter team fights third and leave first when tank cant control enemy team or you are losing.

When you have 2,5 attacks per second and all "Recurve Bow" items:

Every 3 hits you deal 8% enemy max hp dmg and in that time you deal 12% enemy max hp dmg form Madred's. So you need to hit enemy 15 times to kill someone without magic resist. Champions have magic resist but those missing dmg from madred will be conpensated with Wit's End and Sword of Divine.

15 hits with 2,5 hits per second:
6 seconds to kill anyone. In real gameplay this time will be shortened.