I'm a novice to League, silver 3, but I'm also a Ph.D. in chemistry and love looking for creative ways of playing the game. My builds are always wild, and many won't be as effective as the obvious builds, but if you're looking to shake up your gameplay and have a fun time then I highly recommend trying these out :)

When I was looking at different Vayne builds I noticed that a lot of people focus on blade of the ruined king, or building a lot of crit hit chance (standard ADC). I think this misses how different Vayne is from other ADCs; her damage comes her W. Ok, duh, so what? This impacts two important factors
1. lifesteal wont provide Vayne health from her W
2. building attack speed is more powerful than crit hit chance

The first point brought me to items that provide vamp vs. lifesteal. The only two realistic core items for Vayne are Eclipse or Sanguine Blade. I think both could work, but Sanguine Blade provides massive attack speed boosts when one or no champions are present, and another mythic item is better than eclipse later on (more on this later), so Sanguine Blade will be Vayne's first core item. What next?

After deciding on Sanguine Blade (SB) as the first item for Vayne, I was left worrying about having a very low attack speed in lane while building SB. Rushing Berserker Greaves of course helps with this, but it's still much less than starting Blade of the ruined King or Kraken Slayer. How can I increase attack speed?

This is how I decided on hail of blades as the keystone rune. In most cases in lane Vayne wants to trade in sets of 3 attacks to get her W off anyways, and this also allows Vayne to have sudden impact (lethality with her Q). The downside of HoB vs. press the attack is missing out on the later game damage advantage with PtA, which stacks with Vayne's W to do serious damage. The huge upside is Vayne can almost kill any champ in a second at level 3/4 with serrated blade by landing Q plus 2 more attacks.

Note that 11.6 nerfed Ravenous hunger so it's better to take ultimate hunter to reduce the cooldown on vayne's ultimate, especially early in lane when the cooldown is 100 seconds.

Compensating for low AS is why this build needs Hail of Blades.

Now that we're committed to SB as our first item, how does this work out in game?

Serrated Dirk is the go to first item. It simply provides an enormous damage advantage early on since the lethality plus sudden impact provides enough lethality to increase Vayne's damage roughly 6-8% depending on the target level and champ. It also helps Vayne rip through minions, which helps since she has no wave clear.

Vayne simply needs AS to thrive so Berserker Greaves is the next item.

Vayne's core mythic is Trinity Force, and I've found that Sheen provides a huge damage boost given Vayne's constant use of tumble throughout the game. It's 700, but it's more helpful than vamp scepter.

Finish Sanguine blade and move on to building the Rageblade, but remember to buy the cloak of agility BEFORE the rageknife. It's a waste of money to build the other way around since there's no crit hit chance to add damage on hit.

Then finish trinity force which will finally add that spellblade dps and all around boost your stats. I chose this mythic instead of KS because of the spellblade and the additional base attack speed (30% vs. 20%). Again, Vayne needs attack speed combined with vamp to be unstoppable.

After this point just build whatever ADC items make sense in your game, except for infinity edge since Vayne doesn't rely on crit hit chance like other champs.

Other guides for Vayne gameplay are probably more useful. I'll edit this on and off as I play this build more and develop some common moves.

Do not use this build Bot! Sanguine blade only gives bonus attack speed and lethality if one or fewer champions are present, and bot there is almost always another champion (support). This also means if you are ganked by the jungle with sanguine blade you should always run away since you will take a large DPS hit. This also means this Vayne is most powerful pushing lanes or hunting down and assassinating champs in the jungle. This also means she's excellent at ganking mid early.

With hail of blades it's easy to Q(attack), attack, attack, the opposing top lane within ~1s if they stray too close to you. At level 4 with serrated dirk this does ~500 damage, and so should cut any champ's health ~30-50%. If you're up against a fool and they're near a wall then Q(attack if you have sheen), E, attack, attack to get an easy kill.