Alright, this is my first attempt at a build. (Excluding the one I made without an account, but...) If there are problems, please point them out in the comments so I can toy with fixing them. Tips and other comments are also appreciated.

My choices are based on a bit (only a bit) of research through the various Vayne builds, some experience in what's needed, and a few tips on what to look out for. Some choices are a bit off-the-wall comparatively, but I'm trying to counteract the gameplay styles you'll see used.

First off are the summoner spells. Cleanse is a great skill for both chasing enemies down and running away from potential charlie-foxtrots. With the massive use of slows, stuns, and other shenanigans, Cleanse allows you to escape (or chase) champions like Ashe or Taric, who live off of movement-hampering.

Exhaust is a great fight starter or (like Cleanse) chase helper. It can weaken your enemies so they're easier to take on, or cause them to run away with both AI and many players being cowards). It also allows you to chase down enemies more easily, which is something Vayne's meant to be good at.

Those runes are up next. The Quints allow Vayne to take a bit more damage, which is helpful when chasing enemies down through minions or (on hopefully rarer occasions) towers. The Marks give you better damage over time, and also help you pull off Silver Bolts a bit faster (which is a useful trick). The Seals and Glyphs make Vayne tougher, which can be scary for anyone fighting her, as well as boosting the effect of the Quints.

This is the tricky (and most easily adjustable) part of a Vayne build. Grabbing all of Vayne's skills early allows great flexibility on the field, whether you use a skill often or not. Tumble's my first priority in leveling up, though. It gives great maneuverability, and helps with last-hitting minions. Then comes Silver Bolts, a great champion killer, beating up on tanks and squishies alike. Condemn is last, mostly because it's hard to actually get good positioning for it, and it's most useful (in my experience) late-game.

Oof. Let's take it from the top.

The boots are first, because Vayne doesn't have terribly great early-game speed. They also help out that wonderful attack speed.

Then comes The Bloodthirster, with priority towards the scepter. The lifesteal is very important if you want to stay alive as Vayne. Vayne is an extremely squishy champion, but the life-steal cycling through can keep you alive much longer than one would expect, due to Vayne's damage output.

The Black Cleaver's next, adding a hefty boost to speed and damage. This is a turning point, typically, if you've been having a merely mediocre game. The Black Cleaver allows Vayne to build up her Silver Bolts much faster, as well, heavily increasing potential damage.

After that is Banshee's Veil, useful mostly to counter the un-godly amount of slows, stuns, taunts, etc. that you'll see in-game.

After that, is Trinity Force. It has a large amount of highly useful buffs, along with yet more ability to chase down your enemies, which is an ability Vayne can't get too much of.

Then is Infinity Edge, useful for boosting critical hits. And you should've worn by now, unless you're deep in a heated PvP or Intermediate AI match.

The Mastery is fairly self explanatory, boosting most of the needs Vayne has. It can be easily changed if you have different preferences or needs.

I went with a 21/0/9 build, as recommended and often seen in Vayne builds, and here we go into the description of the choices (hold onto your brains...).

First, is Butcher. It gives Vayne a bit of a boost for farming, which can be a chore early game. Then I grab Brute Force, as more damage on a high damage champion is always good. Alacrity is next, to give better speed for Silver Bolts. Then is Weapon Expertise, to help cut down tanks. Next is Deadliness and Lethality, to make the hits count. Vampirism's next, to help postpone those Recalls as long as possible. Then Sunder and Executioner, to make Vayne even more deadly.

Then, I grab Utility. Expanded Mind is useful, as it allows you to keep Vayne's skills in use. Good Hands allows you to get back in the fray faster, but is more of a filler to get to the next tier of mastery points. Then, Meditation for mana regen and Swiftness for more speed.

And a warning of what to expect for those just picking Vayne up.

Vayne will kill-steal. It's simply how an efficient Vayne will play. Either get over your desire to claim kills in a team fight, or pick a different lane.

Vayne can play a very effective low health game, in the right hands. Don't worry about Vayne hanging out in a lane with only five health... it'll be back soon. All you'll do is distract Vayne, and potentially get them killed trying to tell you that they know what they're doing.

Also, Vayne can turret dive. Vayne, if built right, is a highly mobile champion. She will only get hit a few times in a turret dive, so let Vayne go for the turret dive.