Vayne is a ranged AD carry assassin that can also carry. However she has slightly lower range (550). However unlike most carries Vayne is able to assassinate enemies very quickly with her high damage output and mobility. Vayne's passive Night Hunter grants Vayne 40 movement speed when moving toward an enemy hero. Making Vayne very hard to outrun from. Although Vayne has very large damage output with massive help from he passive Silver Bolts she is extremely squishy and positioning in any fight is crucial. I'll just list off some Pros and Cons of Vayne.

I'm not entirely sure on the skill tree but you're maxing tumble as fast as possible while putting 1 point in condemn at level 2. Take your ultimate whenever you can and max silver bolts after tumble ending up with maxing condemn last.

Pros:
-Extremely High Damage Output with Silver Bolts
-Tumble has a very short cooldown. (Approx. 2secs when you use the skill, 6secs to expire.)
-Vayne is able to tumble through Jarvan's Cataclysm, Anivia's wall, and Trundle's pillar. She is also able to tumble through Veigar's stun but will still be stunned at the end of the tumble distance.
-Able to harass very well with Tumble.
-Can burst like an AP caster when fed.
-High Mobility with tumble, night hunter and her ult.

Cons:
-Very Squishy. VERY.
-Usually focused in fights.
-Your death in a team fight could lead to your downfall.
-Condemn is difficult to land and doesn't always go the way you want it too.
-Isn't very fast when she's running away from the enemy as the move speed bonus from night hunter isn't in effect when not facing enemies.

Some tips on how I play Vayne. I may not be the most professional Vayne player but I'm writing this guide and you're reading it. amirite?

Tips: (Most of these are common sense.)
Tumble quickly after your normal auto attack as it will cancel the auto attack cooldown.
You are able to Condemn enemies into turret including the remains of a destroyed turret. Condemn doesn't stun when enemies make contact with Jarvan's cataclysm, Anivia's wall or Trundle's pillar.
Use tumble to maneuver yourself into position for condemn. Practice makes perfect. I recommend laning top or bottom with a good support. The reason for this is because there's more walls to land your condemn. Make sure your support has brush dominance in order to condemn them while they try to gank from the brushes. Warding brushes also helps.
Last hit to get the gold from a minion. Don't push the lane unless you know for sure that you can counter gank when the enemy does.
Be agressive. Very agressive. Unless they have stuns. Don't be cocky it'll be your downfall.
If you're not very good with dodging skill shots dodge them with your tumble.

My choice of runes are Armor Pen. Reds.
Which is self explanatory. Vayne is a fully physical and true damage hero with no skills that scale off AP.
Attack Speed Yellows or if you prefer you can get armor if you feel you're a bit too weak.
Cooldown Reduction blues if you want. M.Resist or Mana Regen also works if you feel you're too weak or running on low mana too often.
Attack Damage Quints or more Armor Pen. but I feel those 9x1.66 Armor Pen. reds are enough.

I don't know if my Mastery Tree is the standard but I take as much damage output as possible with 3% life steal. Since I take 2 doran blades it adds up to 9%. Which is ALMOST 10% life steal!
I also take some additional armor and magic resist in the defense tree as the leftover mastery points.