Here's a build guide on vayne.

Greater mark of Strength:
The amount of damage this gives you early game is crazy. This will help you early game with last hits, and harassing the other opponents.

Greater seal of Strength:
The amount of damage this gives you early game is crazy. This will help you early game with last hits, and harassing the other opponents.

Greater glyph of Alacrity:
The attack speed this gives you is very helpful with last hitting minions. As an ad carry you'll need cs badly.

Greater Quintessence of Strength:
The amount of damage this gives you early game is crazy. This will help you early game with last hits, and harassing the other opponents.

If you go on the ad side it gives you an even better early game, you'll hit harder etc.

When you start out you want dorans blade for more health. Get another one for more life steal and damage.

Berserker Greaves: They give you attack speed and that's what you need with vayne.

Zeal: They give you critical hits and more attack speed

Infinity Edge: This item gives you crazy high hits. Get this as fast as possible. It is amazing early games because of the higher critical hits.

Phantom Dancer: This gives you more critical chance.

Blood thirster: Life steal

Guardian Angel: Even though you're squishy if you die you go down while your team finishes them off.

Pros

+ Ranged Champion: Amazing farmer
+ Very easy to last hit with tumble
+ Condemn: A stun... everyone loves a stun with an ad carry
+ Extreme damage with, and without damage items
+ High damage output early game
+ Final Hour allows invisibility
+ Fun to play


Cons

- Squishy
- Slow attack speed early game
- Slow movement speed
- Targeted easily