I've seen several Vayne builds out there that rush a trinity force, and I don't feel that this is the ideal build. With this build i'm able to 1v1 anyone lategame even other Vaynes, I consistently get triple and quadra kills as Vayne, and currently have a 8.0 kda as Vayne in ranked.

I take attack speed marks, armor seals, magic resist per level glyphs, and arpen quints.
I feel this gives me a strong balance of offence and defence, and I prefer attack speed reds over arpen because it makes getting your combo off much easier in laning, and lategame they help more than arpen reds, it also makes me break 2.0 attack speed with my full build. I take armor seals to boost my armor early game, allowing me to be more aggressive. Magic resist per level glyphs help me with enemy casters late game combined banshees veil. I take arpen quints because i feel they give more than attack speed quints.

I run a very offensive 21/0/9 build as I feel Vayne doesn't need many defensive items or masteries to stay alive due to her impressive kiting abilities plus her amazing stealth from her ult which is very effective at dropping aggro.

I rush an Infinity Edge over trinity force as although trinity force on its own gives more damage (barely) combined with the rest of my items Infinity edge gives alot more damage. In my opinion trinity force is best built alone with tanking items being built after as it doesn't synergize as well as other dps items do. Afterwards I build a zeal, then get a vamp sceptre for basic lanestaying power, finish my phantom dancer. Phantom dancers are an absolutely amazing item on Vayne, the movespeed they gives makes staying alive incredibly easy for me, as well as allowing me to easily chase down the enemy squishies, as well as crit for my Infinity edge, and attack speed for silver bolts. I then get a bloodthirster, as i feel lifesteal is neccesary on any carry as it stops damage from being permanent, Vayne like any other carry can easily farm it up with her high damage autoattacks. I then build a zeal + banshees veil, then finish the zeal into another phantom dancer. Banshees veil is also another amazing item, thats perfect for all ranged carries, if you and your tank play well you should barely ever get hit, and banshees lets you take that one cc that would've brought you down combined with two phantom dancers I find myself never getting caught because of a very high movespeed.

Its become obvious to everyone now that you max tumble first, its definitely her best skill and the cooldown reduction is invaluable, the only decision to be made then is Condemn or Silver bullets first? Condemn gives a slight damage increase and some decent cooldown reduction, Silver bullets gives more damage, alot more and its more reliable. Condemn feels like a one use thing to me, fights usually end before it coolsdown even at max rank, and I fell the benefit of leveling it is alot less than that of silver bullets.

I run ghost, flash like most carries, I build vayne very squishy and this helps keep me out of trouble or if we're dominating them chase, ghost flash feels like the best spell combo in the game, and when against champions without ghost flash, you can kite them so easily, and you get to decide when the fight ends not them.

Vayne like all carries requires alot of farm, you need to be able to lasthit, if you have trouble lasthitting, you can shoot a minion twice, then wait till its lowish and proc the 3rd hit of silver bullets. However this is not ideal as it will push your lane, if you're newer to the game your lane opponents are probably autoattacking anyway/theres no junglers.

I want to attach this to all my guides.
You should never ever call somebody out on not calling an MIA, its your fault you got ganked and didn't watch the map. Call MIA's as a courtesy when possible, but never ever give up cs just to type an MIA.

Vayne is a very strong champion if farmed well, I can carry my team to victory almost 100% of the time with this build, which gives insane ammounts of damage as well as still being able to stay alive due to massive speed from phantom dancers.