Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
This build is highly focused on Attack Speed (maxed out before end game), which maximizes your minion kills which allows you to build quicker. Notice that I max out Silver Bolts at level 9. About that time you have 1.7 attack speed and you are taking 8% of max health every third shot as true damage (unpreventable). About level 12 you are able to finish blood razor which takes an additional 4% max health every shot as magic damage. With such a variety of damage (AD from basic attack, Magic from Bloodrazor, True from Silver Bolts) it is nearly impossible to stop Vayne's damage.
By focusing attack speed extremely quick, you are able to play aggressive a opponent, by tumbling in, getting 3 shots in and getting out before tower hits you. Extremely good harassment technique.
For your last item you can either choose Infinity Edge, which would give you 85% crit chance, or get Frozen Mallet (mainly for the health, but also for the slow).
I just created this build and played 4 amazing games with it, but if you would like to suggest anything or ask, please do.