Hi there! I started playing Vayne the day after she was released. Like many others, I've experimented with different builds, and I feel I've found the perfect set up for Vayne. This build relies on on-hit items, combined with her W and attack speed to melt tanks and squishies alike. The reason you avoid stacking AD is because her ult gives a huge steroid. Building AS items compliments that steroid nicely.

Seals: I choose flat armor seals to help out in the laning phase. They'll help a bit if you have to tank a creep wave or if you're going up against another ranged ad.

Glyphs Cooldown glyphs are mostly a preference here.

Quints and Marks This way you'll have a nice bit of AS without any items early on.

I go with the standard 21 AD carry mastery build. I pick up improved exhaust to help out in 1v1 and team fights. 6 In the defense tree to help out during laning, and the last 3 in support for some minor regen.

Starting with cloth armor + 5 hp potions will let you harass without having to worry too much about recalling. It also allows you to easily build into your razor/bloodrazor.

Boots here are situational. I feel vayne is mobile enough to not need swiftness. If the team is CC heavy you should take merc treads.

Bloodrazor lets you shred tanks, while giving you a nice early game advantage of creep killing and dragoning.

Wits end compliments your W and Bloodrazor by providing another on hit effect and some more attack speed.

Phantom dancer provides AS, Crit and Movement speed, all of which are lovely on Vayne.

You build trinity force a bit late, but by this time you should be destroying the enemy if you're positioning yourself properly.

BV could be replaced with a Guardian Angel if you feel you're still going down fast.

Late game, you're a high speed, max AS killer. With bloodrazor and wits end proccing every hit, and bolts every three, you'll melt any squish that finds themselves out of position. Tanks will die just as fast with your hp-based damage.

Tumble is focused first mainly to provide a decent harass in laning phase. You won't have much AD here if you went Doran's first, but this way you'll have a safer lane.

Condemn...there's not much to say. It's mainly used for the stun. The damage it provides is nice, and the silver bolt proc is great, there's just no need for leveling it past 1.

Silver bolts is the bread and butter of this build. You'll melt everything once you get high attack speed. This comes after tumble, once you have a decent amount of attack speed built up.

Final Hour should have a point added whenever possible. Your ult provides your AD in this build, and lets you tower dive/escape ganks/lose the aggro in teamfights.

A MUST

Flash is needed for a squishy champion like Vayne. Once the enemy starts focusing you, you can flash to safety, then return back to the fight where they least expect it. A must.

MAYBE

Exhaust is nice for many things. It helps quite a bit in 1v1. Also when escaping ganks/securing ganks. Also nice in teamfights when shutting down their carry.

Ghost could be taken as well. Now no one can escape your ganks or tower dives.

Cleanse could be taken. The problem is you're just so squishy that you'll blow up if they focus you enough.

Ignite is helpful in securing kills. Also nice if you know the enemy team will have some form of healer.

Teleport to coordinate ganks or to stop an enemy push.

NO

Revive: You shouldn't be dieing. If you do die, it should happen only a few times.
Heal: Leave healing to the support champions.
Rally: Helpful in team fights, but not worth taking over other spells.
CV: Leave it to the support
Smite: You're not jungling
Clarity: You shouldn't be running out of mana
Fortify: Leave this for tanks/supports.

AS Vayne offers a comfortable laning phase. You can farm and harass as much as you want, taking your time with your 5 health potions. Rushing a bloodrazor is expensive, but Mandred's early on helps with last hitting and early dragon kills. With proper positioning, AS Vayne can kill just as good and maybe better than an AD oriented Vayne.

COMPARED TO AD VAYNE:

AD Vayne has a better, albeit more dangerous, laning phase. You won't have the reliability of armor and health potions, but you will be getting an increase in damage.

I think that mid game, both builds are similar. Both do loads of damage if left unchecked.

Late game, though, is where AS Vayne shines. Your Silver Bolts+Bloodrazor will melt anything with a large hp pool. Wit's end provides a small slice of survivability and a nice increase on damage.

PROS:
Safer early phase
Able to do dragon rather early if coordinated with jungler
More armor for early/mid
Destroys tanks and squishies alike

CONS:
Less damage early phase
Won't be hitting squishies for huge 500+ crits

Be in a good position with your team. Don't run out front ahead of your tank, but don't lag too far behind the group. Plan your position accordingly with the enemy team. If they have an amumu or sona, don't stay too cluttered. If they have a gragas, don't go anywhere near the front. Proper positioning is key with a champion like Vayne.