Hello everyone! I'm Dani105 and Vayne was my first champion that costs 6300 IP and I loved the way she could inflict so much damage in so little time. It was marvelous.

Pros:
- very high damage output
- good mobility
- can take out opponents relatively easy

Cons:
- squishy
- you're likely to get focused

9x Greater Mark of Desolation: these runes will allow you pierce through any armor with ease so you can inflict much more damage.
9x Greater Seal of Attack Speed: with the bonus attack speed these provide you'll be able to hit enemies whithout letting them know what hit them.
9x Greater Glyph of Vitality: as Vayne is squishy you'll love the health bonus these provide.
3x Greater Quintessence of Desolation: more armor penetration? Hell, yes!

These masteries are usuful for anyone who wants to inflict damage.

Ignite is very useful spell for any champion because it gives much true damage and reduces the recieved healing of the target by 50%! Pretty useful against champions with healer, and with Summoner's Wrath it will give you bonus attack damage when it is on cooldown.

Falsh is a pretty goood escape tool, as well as it can give you a kill.

Exhaust is also a good spell if you want to catch up to another champion or if you're afraid of the enemy's damage.

Heal is another useful spell as Vayne is squishy and because of her constant damage output, you'll always be one of the main targets.

Tumble will give a percentage of your attack damage for the next attack making it your primary damage tool. Also useful to evade skillshots.
Silver Bolts will give true damage every third attack based on the maximum health the enemie it hits, making it your secondary damage tool. Consider it as a free and upgraded Madred's Bloodrazor. Note that attacking another target will reset Silver Bolts' debuff counter.
Final Hour will give you bonus attack damage and combined with Tumble it makes you almost untargetable. Also, the bonus movement speed from Night Hunter ( Vayne's passive) is tripled.

I strongly recommend starting the game with a Doran's Blade. Don't start with Boots and potions unless you're pretty sure you can evade attacks. I say this beacause Vayne is really squishy and without the helth boost of Doran's Blade you have a really great chance to die.
After Doran's Blade rush to boots. I say it should be Berserker's Greaves as the build focuses on attack speed. Of course if you wish you can have defensive boots ( Ninja Tabi, marcury's treads). I don't say a Boots of Swiftness is a bad choice but I don't say it's good either. Night Hunter will give you enough extra movement speed for chases and the next items will give much movement speed.
I guess I see your next thought: " Sheen and Trinity Force? Has he gone mad?!" No, I'm not an idiot. I wouldn't suggest if it wasn't worth it. Just think about it: it gives you attack damage, attack speed (!), movement speed and health. Yes, Vayne doesn't benefit frm ability power but, hey, Trinity Force's passive will give you tons of damage even without Tumble. Have something else if you want but I strongly recommend taking this item.
Your next major purchases should be Bloodthirster for life steal, Phantom Dancer for critical strike chance and Black Cleaver for attack damage.
Well, here comes the tricky part. The last item instead of Doran's Blade can be:
- Frozen Mallet if you feel like you have low health
- Madred's Bloodrazor if they have really much health (this is what I recommend the most but it's still your choice)
- another Phantom Dancer for some additional critical strike chance
- another Bloodthirster to counter their tank's thornmail, or to become "immortal" (you can still be killed with this so dont become overconfident, it will give you additional 20% life steal)

Try to stay behind your minions and utilise Silver Bolts. Tumble will also be useful but try to save it to harass the enemy champions.

In a teamfight, try to stay behind your teammates and DO NOT take unnecessary risks. Use Condemn to knock the enemies back to your team ( Night Hunter and the items will give you the necessary movement speed to catch up) or to stun them to the wall. Try to hunt down the squishy and/or low opponents so you can secure a lot of kills and fulfill your role as the primary damage output.

Thank you for reading the guide. I hope it was useful!
Also I ask you to comment your reactions as it is my first guide and I'd like to know what I did right and what I did wrong. Thank you!