There's not reasonable arguments, just that on this patch 14.10 the critical items are completely broken, and this in vayne is no exception. You don't need on-hit atk speed if you can kill any champ with 3 basics. This build is focused on the build crafting, so it is assumed that the player has the basics of adcarrying, Vayne, and ranged dueling in general.
But just in case this is not the case, I will briefly talk about some of the basic concepts that have helped me the most to be successful with Vayne:

ADCarrying Concepts:

-Spacing : You must understand spacing as the way to get the most advantage of your attack range without putting yourself at risk.
To do this, you will press the button that is intended to show the attack range, and you will imagine that range as the true body of your character. Any enemy that enters within this circumference is a potential threat, so you should try to move and attack in such a way so that your personal space is invaded as little as possible.

-Wave Control: Minions are the gratest source of experience,so you must avoid losing waves. Especially in the early line game, you will try to be present in as many waves as possible. For this it is important to return to base at the right time. The right moment will always be when you can crash the wave into the enemy tower, or when the cannon wave is on its way and the line can be neutralized. This way you lose the least amount of minions (gold/exp). It is important not to stop farming in the mid/late game as this can cause you to lose your advantage. so you fight/go to an objective, you farm again, you rotate and farm, whatever you do you farm some line again later so as not to lose experience

-Positioning: You should always be aware of where you are standing and make good movement clicks. Standing in the right place is going to be essential to win the game.
Being closer to an objective than the enemy adc can be a very significant advantage, being attentive to the jungler when the enemy invade him, etc.
In teamfights, like every ADC, it's best to stand behind the rest of the group in a safe place until you can fight properly. But if you are more daring you can stay hidden until you find an opportunity to enter without being seen and kill the most powerful enemies. It is best to always have some ally nearby to support us so as not to be totally focused. All depends on context.

Sometimes you could get saskiogosued and kill everyone 1 vs 5 but it happens 1% of times the rest of attempts you will just die so i higly recomend not to try it UNLESS that it is part of the outcome of a late teamfight and you are the only hope

-See the ***cing Map: See the ***cing Map.

-Track the Jungler, use your wards.

Vayne Basic's:

-Q's Poke: You can Poke using your Q. You must wait for the enemy to last hit a minion and poke him, then quickly back away before he can return the damage.

-Q's AA Reset: If you use your tumble on a wall you will reset your autoatack, it culd be usefull if you need to get an extra hit in an exchange

-E Condemn: This is the most usefull habilitie but it requires a very good reflection. Using it properly you can deny 99% of the Dash, Stuns or mass control resources that could be used on you. Examples of this are the phanteon stun, you must press conemn almost at the same time as the jump animation starts,
this way you won't be stunned. It works with the jump of Alistar, Leona E, and many other all in habilities.

Another thing to keep in mind is that there are many more structures on which you can use condemnation than you could imagine to stun the enemy, for example, destroyed towers.

You can use condemnation to finish off an enemy who has left with very low hp too. This is because you can activate it immediately after a basic, so it has no charging time and its damage can count as an extra basic. Also keep in mind that Condemn applies damage twice: when the projectile hits and when the target hits the wall, so all of these aspects of Condemn can help you to ensure a kill.

-Ultimate: You can take advantage of Vayne's ultimate in many ingenious ways,
you can even seriously confuse the enemy. The basic mechanic of Vayne's ultimate is that once you press R, you become invisible for a while. Invisibility is canceled once the timer has run out, or once you make your next auto-attack.
What you do during the time you are invisible is what is important, so you must use that little time in the best way possible.
A common mistake for novice players is to enter invisibility and immediately cancel it with an auto attack. this should be avoided at all costs since it considerably reduces the time and usefulness of our ultimate. The way to use it correctly is: Become invisible -> Walk to a space where we are safe or where we outplay the enemy -> click autoattack once positioned to become visible again

some Ultimate Tricks:

a) While an enemy is chasing you, then you become invisible and walk in the opposite direction to the logical one, this way he will continue walking in the logical direction so you will gain distance and outplay him.

b) On Teamfight, You can use it to reposition yourself and change from a target that is focusing on you, to a weak target that you can kill easily.

c) Context: You come from base and the enemy ADC is still removing plates.
then before entering the enemy's field of vision, you activate Ghost and when you are at the appropriate distance to enter invisible without being seen, you make a surprise entry and kill him

d) You can use the ultimate to move through the bushes without being seen. You can also use the ultimate to make a surprise entry, from the bush you press Q and leave the bush while being invisible, this way you have all the time of your ultimate to position yourself in such a way that you leave the enemy ouplayed and kill him surprisingly


Early Game

Farm minions (gold/exp) is prority over fighting, unless you see an unavoidable oportunity to kill them, or you have to help your team to fight an objetive. Early Game is basically Wave Control thing. If the enemy line is so strong that you can't farm minions gold properly, you should at least try not to lose minons exp. In this case you wait calmly to be able to farm gold well, or you wait patiently to be able to support yourself with your team to be able to beat them.

Mid Game

You want to help your team achieve the objectives that are close to your line. Once one of the two towers has fallen and the early game ends, you must decide if you want to rotate to another line or continue splitpushing. This will be determined by the enemy team. If you are doing well and you have gained a lot of advantage over your line enemy, you will look for whoever has the greatest advantage on the enemy team and you will try to hunt him down to prevent his advantage from continuing to escalate, help your team to do objetives, and basically kill all those ***cings noobs.
If you have had a difficult line and need to continue climbing, you will try to split push until you recover enough, always being careful not to die and looking at the map. Sometimes if there is an important objective on the other side of the map and you see that the enemy adc is going there, it is advisable to try to stay close of your team and that important objective so as not to get the hate of your team,and give advantage to enemy adc... if there is no important objective it's not so relevant to follow the adc enemy and you can continue farming and splitpushing, since in the latter case it will depend on how stupid those on your own team can be if the enemy adc get feed or not.

Late Game

These are the most important fights since if you die you practically lose the game, so you must always stay standing in a safe place and be completely aware of the location of each of the rivals. You will stay as close to your team if there is any threat like Zed, Talon, Twitch or any character that could oneshot you.

Otherwise, you will try to go as unnoticed as possible, but maintaining a safe distance to be able to act in time. In this way, you will seek to enter when you have the fewest possible threats such as Malphite's Ulti, Neeko's Ulti, Ashe's Ulti, etc. If you can hit and stay safe from these abilities before they are cast you should take advantage of every moment.

Depending on the context, you will hit whatever is closest without putting yourself at risk, allowing your team to shield you, or you will enter from an invisible flank to kill the carrys/mages/assassins with low health and high damage, while you team deals with the characters with the most life and the least damage