Theorycrafting: Vayne - The Night Hunter

Night Hunter (Passive): Vayne ruthlessly hunts evil-doers. She gains bonus Movement Speed when moving toward nearby enemy champions.
Great passive, allowing you to chase almost anyone down, especially if you take ghost.

Tumble: Vayne tumbles, maneuvering to carefully place her next shot. She rolls toward the cursor and her next attack deals bonus damage.
A low cooldown skill, though this is your initiate/escape skill. You gain bonus damage scaling off your AD which increases every rank. Max this second.

Silver Bolts: Vayne tips her bolts with a rare metal, toxic to evil things. The third consecutive attack or ability against the same target deals a percentage of the target's maximum Health as bonus true damage. (Max damage vs. Monsters is capped)
Your bread and butter skill, and one reason a full AS Vayne with one or two AD items is very viable. 8% true damage based on max health every second is devastating when you're AS-capped at 2.5. Max this first.

Condemn: Vayne draws a heavy crossbow from her back, and fires a huge bolt at her target, dealing damage and knocking them back. If they collide with terrain, they are impaled, dealing bonus damage and stunning them.
This is your main CC, but it is highly terrain-dependent. It is reminiscent of Poppy's Heroic Charge, except in ranged form. Like Tristana's ult, you can also use this to escape. The cooldown and mechanics of this skill means you get to use it once in a teamfight, and maybe another time for when you're chasing. Max this last.

Final Hour (Ultimate): Readying herself for an epic confrontation, Vayne gains increased Attack Damage, stealth during Tumble, and quadruple the bonus Movement Speed from Night Hunter.
A bit lackluster, but great for chasing. Learning how to use the stealth mechanic (a VERY short stealth period) will allow you to juke or even close the gap safer when ganking. As with any other ultimate, max this ASAP.



Masteries
21/0/9, skipping Lethality as your main source of damage is proc-ing Silver Bolts as much as possible.

Runes
Greater Marks of Desolation
Greater Seals of Alacrity
Greater Glyphs of Alacrity
Greater Quintessence of Fortitude OR Desolation

Core Items
Phantom Dancer
Frozen Mallet
Recurve Bow (Build into Madreds or Starks, depending on what the team needs)

Default Build - Leaguecraft Vayne Builder

Reasoning:
Cloak and Dagger - allows you to have CC reduction, while maintaining your attack speed.
Berserker Greaves - with the release of the Tenacity stat, there's no reason to always stick with Merc Treads, unless the enemy team is AP-heavy.
Phantom Dancer - Even though Vayne gets a movespeed bonus from her passive, this allows her to gank better, and help her reposition faster. Also, the AS bonus is always welcome.
Madred's Bloodrazor - AS and a bit of armor. Plus, the bonus magic damage doesn't hurt either.
Frozen Mallet - Increases her ganking/chasing ability.
Banshee's Veil - Well, duh, best item in the game.

Viable Items:
Mercury Treads - AP-heavy teams.
The Bloodthirster - Mid/Late-game lifesteal

The Black Cleaver - Though she doesn't need the armor reduction, it's still a DPS increase.
Sword of the Divine - For dodge-happy champs
Stark's Fervor - If your team needs it, replacement for Madred's
Wriggle's Lantern - Early game lifesteal
Quicksilver Sash - Situational. If there's a Vlad/Malz/Morde/Warwick or any other champion with a troublesome DoT/CC, get this. Replacement for Banshee's Veil.