Hi, I'm DisturbedFox, a Gold I player who mains AD Carry. Vayne is one of my favorite champions so I decided that my first guide should be about her.
Vayne is a ranged AD Carry who is one of the deadliest champions late game but is somewhat vulnerable early. Most of her strength comes from true damage of Silver Bolts and low cd Tumble which makes her very mobile. She is a good pick in both SoloQ and arranged 5v5s.

Greater Quintessence of Life Steal: Lifesteal quints are the best choice for AD Carries right now. 2 of those is enough to sustain yourself in lane, especially if you're rushing BotRK.
Greater Quintessence of Attack Damage: Instead of 3 life steal quints, take one AD quint. Why? Because 9x AD marks + one AD quint give exact amount of AD needed to last hit ranged creeps under turret at level 3.
Greater Mark of Attack Damage: Standard marks. Bonus AD helps with last hitting.
Greater Seal of Armor: Standard choice of seals. You obviously need armor.
Greater Glyph of Magic Resist: Might want to swap those for MR/lvl if enemy bot lane has no magic damage.

Flash: Best summoner spell in the game. The amount of utility it provides is too good to not take it. You always want to have this.
Barrier: Your standard choice for second spell. The shield is very good.
Cleanse: Take it if enemy team has lots of CC.
Exhaust: Also a good defensive spell. Take it if your support is going with Ignite and enemy team has someone like Zed who needs to be exhausted.

Passive: Night Hunter
Explanation: Increases your movement speed when looking towards enemy champion.
Helps chasing people down.
Note: Bonus MS immediately fades away when you face away from any enemy champions.

Q: Tumble
Explanation: Short gap closer, bonus AD on next hit after activation. Costs very little mana.
Use this to reposition yourself. We want to level it til rank 2 early and max second.
Note: You can tumble out of Crystallize and Cataclysm.
You can't tumble through walls.
Tumble resets auto-attack timer. Use this to last hit multiple minions.

W: Silver Bolts
Explanation: Bonus flat and % max HP true damage after 3 consecutive hits on a target.
This is what makes Vayne so deadly once she gets her items as she just shreds through tanks.

E: Condemn
Explanation: Knocks back target, dealing physical damage and applying one stack of silver bolts. If target collides with terrain, it takes same amount of damage again and is stunned.
This is a great self-peel or initiation ability.
Note: Use tumble to position yourself to land a condemn that will stun your target.
Targets get stunned if they collide with turrets or inhibitors.
Does not work on Crystallize and Cataclysm.
Can interrupt dashes if timed correctly. This includes Headbutt.

R: Final Hour
Explanation: Gives bonus AD upon activating, MS from your passive is tripled and tumble grants 1 second long stealth.
When Vayne ults, you know things are about to go down. Bonus AD is obviously great, more MS means you can chase down opponents faster and stealthing breaks down focus.