Buildwise, you can help with the weak early game of a champion like Vayne by buying one or two doran's blades early, and having an early vampiric scepter. It's always a difficult call, because you're delaying the point at which she hits her late-game-unstoppable-angel-of-death stage, but it's always worth it if it prevents you from being crippled early.
You also want to try to farm as much as possible on a champion like Vayne. Basically relentlessly go for any farm you can get, since the sooner you reach your lategame stage and then group up, the more likely your team is to win. Your goal to shoot for should be around 100 minion kills per 10 minutes of the game - that's nearly an idealized number which is very difficult to hit, but it can give you an idea if you're missing farm too much.
If Vayne has Bloodthirster, Infinity Edge, Phantom Dancer, Last Whisper, and a defensive item, the game is effectively over for the enemy team. She's incredibly difficult to stop at that stage.