Sup. You've made a good decision playing vayne. She is the most amazing character in the game and I for one completely destroy with her. If you follow my purchase order and ability order, all you gotta learn to do is get your tumbles down pro and you're good to go :)

Pros:
Good early game.
Amazing end game.
Amazing ganker.
Chases down enemies like none other.
Absurd damage.


Cons:
Slow early game, hard to get away.
Squishy.

I just use EXHAUST and GHOST. Up to you, i'm not going to tell you what to use, but those are two good choices IMO.

Wait for opportunities. Don't just jump into a group of three people at full health expecting you'll annihilate them...I mean, you will if they happen to not see you, but you're extremely EXTREMELY squishy. Plan stuff out.

Pretty simple. Tumble for damage. But, if you have your ultimate, time your ultimate JUST before your tumbles so you can get the 1.5 second stealth so they don't know wtf happened, then you also get the damage buff. Also if you're near death throw in an condemn if you can for them to get away from you, or if they're near a wall condemn them into a wall for the extra damage and stun so you can destroy them.

Freaking tumble. It's unique in that you can use it to escape, dodge stuff, and chase people down. Get GOOD at your tumbles. Get used to using them with your mouse and etc etc etc.

Vayne is easy. Auto attack and get good at tumbles, at use my purchase order and you're good to go. Have fun with your penta kills, later.