Hullo, this is my first build. After playing Vayne for a lil while I felt like making a build so here it goes. I don't usually get to much survivabilty, you just have to make it up with you damage.

Pros:
-AMAZING burst
-Almost unbeatable in 1v1
-Great harasser
-Great escaper
-One of the best chasers in the game
-Badass

Cons
-Very squishy
-running out of mana stops you from harassing early game
-Targeted first, as she deals a lot of damage but cannot take very much.

Flash - Great for escaping as well as chasing, can also be used to position yourself correctly for Condemning someone into a wall.

Great for chasing as well as escape, again, another multi-functioning spell.

Exhaust - Good for 1v1ing I wouldn't recommend it because that's all it's good for.

Ignite - Great for killing runners and not having to turret dive, but Vayne is a good turret diver as you can just tumble away fast.

I use a basic offense 21/0/9 build, however, if you want to go into defense you can pick up the dodge and get some extra survivability. For offense you don't have to take Spell Pen, if you don't take points out of reduced CD's and put it in increased crit damage.

Doran's Blade is a good starter, but you can skip right to boots for chasing. Swiftness help a lot for chasing as well as escaping but Berserker Boots are good too. Next is Sheen, this is essential for getting good burst damage after a Tumble. Then Bloodthirster is the way to go, build up the Scepter first it will help you stay in lane longer since it will be early game when you get it. Next is Sword of the Divine, works really well with bolts for passive damage, also really helps with the attacks speed. Black Cleaver is next, great for armor stackers, but if you are fighting more casters try Banshees. Finish up your Trinity Force for obvious reason then finish with an Infinity Edge.

R > Q > E > W
For skills make sure tumble is your first priority as it is great for harassing and will deal most of you damage. At level 3 though, make sure you have all your abilities as you will be able to pick up a first blood easily. After maxing Tumble go right for Condemn, this will be more beneficial because Silver Bolts won't be great until max level anyway.

Play somewhat aggressively however carefully, you will die fast. Early game use Tumble to harass in lane. Vayne is a great solo but is also great with any champion with a stun, they stun once the enemy is near a wall, you hit E and stun them again. Try to avoid using E while chasing, it could ruin your chances of getting them, but if they are within kill range, use it. Try to use your ulty midway through a teamfight, not at the start, in case there are any runners that need a chasin'. Vayne is also a great assassin, if you see anybody that is pushing a lil too far, no matter the health, you can just about always bring them down.