Do not overestimate Vayne's mobility. Night Hunter's bonus movement speed grants no bonus while running away from enemies, and Tumble doesn't go on cooldown until you actually attack an enemy which essentially adds 6 seconds of cooldown that you can't reduce with cooldown reduction when you are using it to run away.
Note that Tumble's extra damage only activates upon attacking enemy units, not structures.
You can escape in the midst of a battle by using Final Hour and Tumble to stealth and confuse the enemy. It is recommended to change direction than the one you where running in or to choose an alternate route.
It is recommended to bring the summoner spellsGhost and/or Flash as she has no escape method other than Final Hour in conjunction with Tumble, which only stealths for 1 second, which does not allow her to travel far. These two summoner spells can also help with chasing enemies as well. Since she is squishy, it is highly recommended to use them.
One of the above can be substituted for Cleanse. If you are stunned or are focused down with crowd control like Exhaust you can escape without taking as much damage as you would have and may even be able to come back in and position yourself again in the teamfight so that you won't get focused.
Building Sheen or Trinity Force can add some significant burst to Tumble. Starting with Phage provides much needed survivability and can easily net a kill should you obtain a first hit proc when your lane is pushed. Building Zeal first grants her added mobility and attack speed to more easily farm and proc Silver Bolts.
Vayne has zero abilities which scale with ability power, so consider this fact when deciding what order to buy items in.
A commonly held misconception is that due to Silver Bolts dealing true damage, Vayne does not need to purchase Last Whisper to deal with tanks, instead only needing more attack speed. This is somewhat not true, as most calculations with endgame builds(based on low elo games) have True Damage only composing around 7-10% of her total damage. Moreover, an attack speed reliant build without a Last Whisper is very easily countered by a Randuin's Omen, as it will occasionally negate 35% of attack speed as well as have a strong amount of armor that the Vayne player does not have penetration for.
Consider when to favor Attack Speed over raw Attack Damage. In some instances, you can have an excellent damage-output with Silver Bolts combined with high Attack Speed items such as Madred's Bloodrazor, which compliments with its on-hit percentage magic damage off maximum HP.
Be warned, Attack Speed builds are extremely vulnerable to Attack Speed reduction items and skills.
Infinity Edge provides a substantial boost to Vayne's damage output from auto attacks. Remember that critical hits don't proc from Condemn and don't scale from Tumble's bonus damage.
Choosing someone such as Miss Fortune or Caitlyn who have strong early games can easily deny Vayne from farming as Vayne has a relatively weak early game. Avoid pushing the lane as 薇恩的Tumble makes her an exceptional farmer under turret, and has strong chasing potential.
Vayne's entire kit is focused on dueling (or 1v1ing) and chasing so deny her the potential to duel with you and her kit will naturally round out lategame when teamfights become dominant, where the fights become more stationary and targets become harder to focus.
Once Vayne obtains Final Hour at level 6, her dueling potential increases exponentially and she essentially "jumps" to her mid-game potentially immediately before most other Attack Damage Carries. The Attack Damage and movement speed boosts are huge given how early in the game it is and stealth detection is much harder to afford earlier on. Respect her presence at level 6 if you haven't pulled a significant advantage over her and avoid dueling her if possible.
Silver Bolts is relatively easy to counteract contrary to popular belief.
Frozen Heart is extremely detrimental to Vayne because the armor portion of the item counters her lack of magic damage and the long-ranged -20% attack speed aura is practically unavoidable in teamfights. Randuin's Omen is also especially useful against Vayne as one proc of slow will significantly cripple her true damage and mobility. Because Vayne relies on her mobility in order to survive in teamfights due to her short range, the movement speed slow will make her an easy target to focus. As such, even building an early Warden's Mail will have noticeable effects against her.
The same case goes for lifesteal and high health regeneration; if the target's lifebar isn't noticeably large but is constantly renewed from either high lifesteal or abilities such as Sadism, the damage from Silver Bolts becomes significantly less noticeable.
Battling her only in teamfights forces her to switch targets, resulting in fewer Silver Bolts procs.
Mages with targeted burst damage/crowd controls such as LeBlanc or Ryze can easily dispatch Vayne as her mobility and Tumble are primarily anti-skillshot oriented. Targeted abilities that apply targeted hard crowd control's such as 沃里克的Infinite DuressInfinite Duress and 玛尔扎哈的Nether Grasp prevents Vayne from retaliating with her mobility and lifesteal resulting in an easy kill.