Hello there!
I'm Cadam59 a Gold Vayne main. I have been playing Vayne since she was released and been through thick and thin with her. I'm making this guide for the less experienced Vayne player to get a bit of a you know how to play Vayne feeling.

Here's the link to my OP.GG: euw.op.gg/summoner/userName=Cadam59

Obviously you want to start out with the normal ADC starting items.

Statikk Shiv:: You want to get Statikk Shiv since it synergizes extremely well with your tumble.
Infinity Edge:: Right now Infinity Edge with Statikk Shiv is one of the most broken combinations on Vayne. Since you will almost 3 shot people at level 9!
Trinity Force:: Same as with Statikk Shiv, Trinity Force almost adds up to 500 damage to your Tumble AA.
Phantom Dancer:: As the name says, you want to dance around in the teamfight. The extra movement speed it gives you is required on Vayne. And the stats are really nice as well!

You want to put some points into your Silver Bolts before you start maxing out Tumble. So you will have enough damage to trade with AA + Q + AA.

Condemn last since the damage it does and it's cooldown isn't necessary in early levels.

In the laning phase you want to farm up as much as you can. Most ADC's out range you so you will have a big disadvantage in the lane. Try to poke with AA's when the enemy ADC hits a minion. After that go with an AA + Q so you get your silver bolts proq.

DO NEVER TRADE WITH AA + Q + E YOU WILL HAVE NO MANA LEFT!!!

In teamfights position yourself in the backline of your team. And wait for the right opportunity to ult + tumble in the enemy backlines to kill them. Always attack the CLOSEST target. Always use the invisibility of your tumble to re-position yourself. Do never Auto Attack immediatly after using Tumble!