Pros

-Strong late game
-Lots of outplay potential
-If you do well people will call you Imp/Doublelift etc.

Cons

-A bad support will weigh you down 9/10 times
-Easily counter picked
-No immediate burst damage

I play Vayne because she's fun. I remember looking at my ranked stats and thinking, no way did I play that many games as Vayne this season. And yet I know I did.

Vayne is strong late game, [you've never heard that before] and she's also the only adc with a targetable stun pre level six.

If the enemy team is mostly squishy, BOTRK becomes optional, but remember that it has strong synergy with Vayne and you can build it anyway.
QSS is very useful and I would buy this item instead of taking Cleanse as a summoner spell.
(Cleanse does not remove suppressing abilities such as Warwicks ultimate).
Infinity Edge is not always necessary but it increases Vayne's damage immensely.

There's a lot of people that max Silver Bolts first and I know the reason why. However, it has an undesirable trade off of leaving your Tumble on an excessively long cooldown, this means it's a lot harder for you to reposition in fights and god knows you have a lot of those.
I have heard of this stupid thing of maxing your condemn first which was apparently done in the LCS, and here's what I have to say about that. You will not always land your condemn, and you're removing all of the barely anything you have in your early game.

-Solo queue
If you play Vayne in match me with ******s, do not expect said ******s to peel effectively.
If you have an opportunity to split push in the mid game, do so.
Never counter pick yourself on purpose.
-Ranked 5's
If you're in Curse Voice, Team Speak, Skype etc, make sure to scream at your team when you die.
Also make sure you get a support that can synergise well with Vayne or can peel easily.

Don't counter pick yourself.
Try not to fight early game.
Always type in capslock because your team sucks.
Watch the enemy team composition and build accordingly.
Buy wards as Vayne top otherwise your team will abuse you for dying, actually they'll do that anyway.
Vayne in solo q isn't as effective because you need to rely on your team.
Vayne in ranked 5's isn't as effective because you're constantly yelling at your team.

Have a nice day, stay away from edgy memes.