This is a simple DPS (mostly burst damage) Vayne build I use. The goal is to get as many kills as you can early game, so you can have the power to shut down late game as well. You should probably play Vayne as a mid champ, or play in bottom lane with a tank or a support so you can keep your gold up. If you're mid, ganking after level 6 is a great idea. You can enter in with your stealth tumble, condemn them into a wall for a stun, and easily pick up a kill. Enjoy reading through this build.

The runes I have listed are likely not the optimal runes. Though note that for vayne, your marks MUST be armour penetration, where as the seals and glyphs can be just about anything. Choose according to how you like your play style.
As i've noted, I like playing vayne as a burster, therefore, i get cooldown reduction, to tumble more often in the early game.
The flat health is to make up for her squishiness early game. Sometimes that extra 50 hp can be the 50 hp you need to stay alive.
The armour penetration is a must! It lets her tumbles do insane amount of damage early. Most champions will have less than 20 armour up until about level 6. This means, until level 6, you are doing true, if not, bonus damage with every attack.

Once again, the masteries I have listed here are likely not optimal, but suit the playing style I like with Vayne. For a champ like Vayne, you must have 21 offensive masteries, most likely, in the order I have placed. However, if you prefer your Vayne to be less squishy early game, then go ahead and plug in 9 mastery points into defense, picking up bonus health at every chance. Or, if you're like me and prefer flash to ghost on Vayne, then go with 9 mastery points in support, picking up less time spent dead (If you're mid this is a VERY important mastery skill), and the bonus rune time. The bonus rune time is great, because if you're a bit behind on farm, you can always hit the jungle after about level 8 and just free farm there, picking up red and blue buffs. Of course, if you have both buffs, ganking would be the best decision you can make with Vayne.

These items are the best layout for quick burst damage, especially early game.
Open up with a dorans blade. This is a great early game item for Vayne. It gives her that extra bit of health she desperately needs, gives her 3% lifesteal which can altogether replace the use of potions, and 10 attack damage, which only gives her even more stopping power early game.
Then after farming, wait until you have about 2000 gold so you can go back and pick up a B.F. sword and boots of speed at once. I personally always try to get my B.F. before I get boots. If you feel like you're being harassed far too often, then go with the boots before the B.F. sword.
After your B.F. sword and boots, grab a vampiric scepter. This will give you a ton of more sustainability. You likely won't even have to go back to the fountain after you get into a fight with someone because you'll be able to farm back your health quickly now that you have 18% total lifesteal + the B.F. sword for damage.
Now finish off your black cleaver. The black cleaver stacks amazingly with your silver bolts. You can reduce the opponents armour by 45, plus with the extra 24 armour pen you have and the 10% armour pen mastery, that's a ton of bonus damage per hit!
Now try and finish your infinity edge as soon as possible. Grab a B.F. sword first, then either a pickaxe or a cloak, depending on what you feel you want more. With that extra crit percentage, extra crit damage, the armour reduction on the black cleaver, and the armour pen masteries and runes, you can finish off an enemy in no more than 5-6 hits. Absolutely beautiful.
You should be nearing the end of your core build, grab a bloodthirster and just farm. Try your best to stay out of harms way until you get your bloodthirster stacks up. With your bloodthirster stacks at full, you'll have an immense amount of base attack damage, as well as a solid 31% lifesteal, an amazing amount to keep you from needing to go b unless you buy.
The next item is a luxury item basically, but it's an amazing item on vayne. You will never lose a 1v1 as long as you are the initiator of the first. Start off with sheen. This will give your tumbles DOUBLE damage. Your tumbles without crit, should be doing about 400 without sheen. With sheen, you'll be doing 800, and not only that, if you crit, you could be doing up to 1.8k damage (assuming they have no armour). Get a zeal next. The movement speed boost, the attack speed, and the crit percentage are the three things your vayne needs at this point. It'll only let her chase and finish off enemies that much quicker. Finish your trinity force and sit back and relax, and just keep tumbling. Watch your enemies' health bars vanish.
Of course if the game has gone on long enough, sell your doran's blade if you haven't already, and grab a phantom dancer. Sure you'll lose a bit of hp, lifesteal, and damage, but now, you're moving faster than most champs do WITH ghost. You can chase down anyone, and finish them off in less than a second with the amount of burst damage and crits you're doing.
OR
Instead of phantom dancer, grab a banshee's veil. The single most useful defensive item. It could save your life every 45 secs. A Vayne that hasn't been cc'd, is a happy Vayne.

Skill sequence is basic. Every vayne knows that tumble is your bread and butter. Max that out as soon as you possibly can.
Grab your ultimate skill at every opportunity, which means level 6, 11, and 16.
Many vayne players I see or have read guides on, seem to max out their condemn next. I feel like this is unnecessary because I only use my condemn for the stun, not the bonus damage. If I was to auto attack and crit, it would do much more damage than if I used condemn. Therefore, I only grab a point in it at level 3, and max it out last.
Your silver bolts are absolutely beautiful, and should therefore be maxed out second. The true damage is amazing, and actually a very large amount, only scaling larger as you level it up. If you auto attack twice and tumble for the third hit with the true damage, you could force the champion to his base, or even kill him. Very simple. I go for burst damage output, and therefore max out silver bolts second.

Flash and exhaust.
Simple.
Flash lets you get away over walls if you need a quick escape, or you can flash into a team fight, and devastate your enemies after they've blown off all their cc.
Exhaust lets you slow down an enemy trying to get away, or you can use it to be able to solo an enemy after you've already got your health fairly low.
You can substitute flash for ghost if you want the extra movespeed to gank a lane from mid quicker, or you can take cleanse, because if vayne is CC'd, she's dead. She's two squishy to live through even a 1 sec stun.
Ignite could be used too for an early game kill. Burst your enemy down and leave them burning to secure a kill for first blood.

Vayne is one of the best Burst AD carries out there. Very versatile, and a devastating addition to a team fight. Remember you shold never engage a team fight. Wait a few seconds after one has erupted and then enter, to ensure you won't be cc'd. jump in and burst your enemies down, one by one. I hope this guide has helped.