Vayne, like most ranged carries, can utterly melt an enemy team. She can also be destroyed in about two seconds flat.
DO: Fight 1v1 duels when you are sure you can take them down, or have room to kite, and know that their team is not enroute.
DO: Pick one and only one target to attack in a team fight, and only move on to the next when they are either dead or out of range in a position that would be bad for you to chase.
DO: Harass as much as possible in your lane at the beginning to deny them experience or get first blood. One lucky tumble crit is all it takes to half a level 1 hero's health.
DO: Build Sheen if you are getting a good farm. Going ahead to Trinity Force afterwards is optional depending on HOW good your farm is, but Tumble + Sheen proc makes your midgame burst absolutely unreal against unsuspecting enemies.
DO NOT: Ever use Condemn unless you are guaranteeing a kill or a stun that will lead to a kill. Its value for saving your ass is simply too high to ignore, and its cooldown too high to waste.
DO NOT: Enter a team fight if you have even the smallest suspicion that they are saving CC for you. That is what your team member with the really really tiny health bars is for.
DO NOT: Tumble next to corners. You will almost definitely get hung up on the wall.
DO NOT: Switch up targets constantly. You need the three hit to melt people down.