Ok guys this is my first guide.
When playing Vayne, the first thing you need to know is that her EARLY GAME IS THE WORST, no attack speed or considerable AD to harras, so focus in farming until we get level 6.
After getting your cool ultimate and at least http://edge2.mobafire.com/images/item/berserkers-greaves.gif and http://edge2.mobafire.com/images/item/vampiric-scepter.gif you can start initiating some plays on bottom lane.
On mid game you should already have your http://edge2.mobafire.com/images/item/statikk-shiv.gif, why this item? because electric shocks can criticaly strike and it's a great tool for farming, and also your http://www.mobafire.com/images/item/zeal.gif which will be upgreaded to a http://www.mobafire.com/images/item/phantom-dancer.gif. while in mid game make sure that you pick up kills as any adc would need it, keep tanks away from you with your E and don't hasitate on focusing them if they keep bothering, your tru damage will probably make them go back, giving your team a chance to jump into their APC and ADC. Remeber to farm up, specially if your team is not doing very well, you need to get AD in order to rock late game!
Late game is all about going all-in with your ultimate, it has a very low cooldown so if you catch someone alone in your jungle or river just use your ultimate and pick up that kill! you will be able to use it again on a latter teamfight.