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 7 seconds of cooldown that you can't reduce with cooldown reduction when you are using it to run away.
Tumble can cross impassable terrain such as the small ledge near dragon pit if you position correctly.
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 were running in or to choose an alternate route.
Because she is squishy, it is highly recommended to opt for more defensive summoner spells, such as Heal, Cleanse, or Barrier. Flash is very desirable. Final Hour in conjunction with Tumble only gives stealth for 1 second, which doesn't make for a very good escape. These summoner spells can also assist in chases.
Condemn could also be used when Vayne loops to the back of the target and knocks them towards allies.
Using Condemn in jungle fights can be much more effective than in lane fights due to the tight spaces making it easy to land the second effect and stunning an opponent.
Blade of the Ruined King is considered to be a core item in every Vayne build due to its fantastic synergy with Silver Bolts, not only due to the attack speed, but also because of the passive which has synergy with the health shred from Silver Bolts, not to mention the lifesteal. Once Vayne has this item, she can 1v1 almost every champion, no matter how tanky that champion is.
In addition, Vayne can easily compensate the lack of raw AD of this item, due to Final Hour's temporary AD boost.
Since all of Vayne's damage is physical, it is a good idea to buy armor penetration items like Lord Dominik's Regards or Mortal Reminder to allow her damage to scale into the late game. The synergy with Silver Bolts makes it great for taking out tanks.
Youmuu's Ghostblade is a viable option for even more mobility and to give a boost to Vayne's early/mid game damage potential. It is less of a DPS item, and more of a burst item that can be used against teams which do not have a lot of tankiness but have a lot of mobility.
Infinity Edge provides a substantial boost to Vayne's damage output from auto attacks. Unlike other ADCs, however, it is recommended to not rush this item, as Blade of the Ruined King is a better rush. Remember that critical hits don't proc on Condemn's damage.
The Bloodthirster provides much needed lifesteal to aid her survivability and scales with her Tumble and Condemn. It can be used to complement Blade of the Ruined King as a lifesteal item, giving Vayne insane amounts of dueling potential. However, it is not recommended to replace Blade of the Ruined King as the synergy that this item has with Vayne is just too good to pass up. While as a complement, Vayne has to sacrifice one of the items on her core build, which may hurt her overall damage.
Death's Dance presents a better alternative due to its damage delay passive and the cooldown reduction.
Building Sheen or Trinity Force can add some significant burst to Tumble. Starting with Phage provides much needed survivability and can assist in running from or toward a target if Vayne procs it on an enemy minion. Building Stinger first grants her added CDR for Tumble and attack speed to more easily farm and proc Silver Bolts.
Do take note when building Sheen that Vayne has one of the lowest base AD in the game, hence it's proc won't deal too much damage.
Due to Silver Bolts, one can build Vayne fairly tanky with just a Blade of the Ruined King as her damage item. By using items like Frozen Mallet, Randuin's Omen, and Banshee's Veil, Vayne becomes surprisingly tanky while still dealing a lot of damage. This build is not recommended most of time because Vayne already has so much self peel and mobility that building tanky is not necessary for her. Also, Vayne does significantly less damage with a tanky build - this may sound obvious, but for those who know how to kite and reposition themselves well enough to avoid most of the damage, a glass cannon build will be infinitely more profitable.
Essence Reaver works well as a situational item if you find yourself using up too much mana throughout the game (although Vayne doesn't really need that much mana), and the cooldown reduction it provides is also good for Vayne since it will allow her to use Final Hour more often.
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 Vayne'sTumble makes her an exceptional farmer under turret, and has strong chasing potential.
Vayne's entire kit is focused on dueling and chasing, so deny her the potential to duel with you and her kit will naturally round out late-game when team fights 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 spikes 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.
Vayne is one of the most powerful duelists in the game and is well known and feared as one of the most powerful marksmen if/when she reaches full build. It is critical to keep her early and mid game crippled.
Marksmen are usually easy prey to one-burst-wonder assassins, especially Zed and LeBlanc. Vayne is by far not in this category, her ability to carefully move around the battlefield, drain-tank while evading attacks with stealth from Final Hour and bursting/peeling with Condemn makes her complicated to kill by surgical, tactical and careful assassins as she can often prevent their abilities to properly flow for a combo.
Lee Sin's kit provides extreme stealth detection and Cripple shuts down Vayne's mobility. With the correct build, Lee Sin can usually one-shot Vayne late game.
Silver Bolts is not that hard to counteract contrary to popular belief.
Her Silver Bolts procs rely on her attack speed. Champions with attack speed slows such as Malphite and Nunu can mitigate Vayne's auto attack and Silver Bolts damage significantly along with having kits that counteract Vayne extremely well.
Frozen Heart is extremely detrimental to Vayne because the armor portion of the item counters her lack of magic damage and the long-ranged -15% attack speed aura is practically unavoidable in team fights. This item is arguably a better option in dealing with Vayne, as it does not provide HP, thus making Silver Bolts less effective.
Randuin's Omen is especially useful against Vayne as one proc of slow will cripple her true damage and mobility. Because Vayne relies on her mobility in order to survive in team fights 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. Come mid-late game, Randuin's crit reduction will reduce Vayne's damage output even further as critical strikes are an important part of her damage.
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.
Teemo can completely shutdown Vayne's true damage output with the help of Blinding Dart, especially by surprising her with Guerrilla Warfare. This is even more useful if Vayne'sCondemn is recently used due to its fairly long cooldown.
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 such as Warwick'sInfinite Duress and Malzahar'sNether Grasp prevents Vayne from retaliating with her mobility and lifesteal resulting in an easy kill.
It's recommended not to fight Vayne in the jungle as there are more walls for her to stun with Condemn.
Taking a Control Ward with you is useful against Final Hour as her stealth will be useless, shutting down her primary method of reaching squishier targets of interest. Oracle Alteration also helps detect Vayne albeit to a lesser extent.
Vayne can be a very powerful top laner against tanks, so when you see your enemy pick Vayne, especially if the enemy team has already selected another marksman, ask your jungler to pick a tank just in case she decides to go top so you can pick a damage top laner who can fare against or even kill Vayne.