Hello Summoners, I'm an AD Carry main. Vayne is one of my favorite champions due to her massive damage and mobility. First off this guide is a WIP. I will work on it more when I get a chance.

Late game hyper carry
High mobility
Rewarding if played correctly.

Semi-Weak Early Game
Unforgiving with mistakes
Takes a lot of time to perfect her kiting

Start Doran's Blade, Health Pot, Yellow Warding Trinket. Just focus on CSing early game. Harass with auto attacks when you can. Try not to fight to much early because you will get out traded by most lane opponents at this point in the game. You need to get at least 70 CS at 10 mins to not be far behind during mid game. Focus on finishing Blade of the Ruined King as your first item.

At this point you should have at least a Blade of the Ruined King, Boots, and a zeal building into Phantom Dancer.

This is where you shine. If you play well enough at this point in the game you can carry your team on your back.

If you don't get 3 AA's off to trigger your Silver Bolts you will be out traded every time.
A good way to trade is Auto Attack -> Tumble into another AA -> Condemn them away. It will trigger silver bolts and push them back to minimize their ability to trade back.

Orb Walking is a must when you play Vayne.

In team fights stay towards the back so you won't get CC'ed and blown up. You're the AD Carry. You need to play safer and smarter than everyone else. Everyone on the enemy team is going to be looking to focus you because you deal the most damage. Be very careful with positioning and stay with your team. Remember, its not your teams fault they didn't peel for you if you tumble in a bad spot and get caught out.

Orb Walking Guide
Advanced Vayne Mechanics
More detail about match ups