Twisted Fate is known for his ability to deal massive amounts of DPS and gank from almost anywhere on the map. This build focuses on getting a lot of really cheap DPS items and then turning around and dealing high, nuke-like MAGIC damage based on ATTACK SPEED. This really messes with tank's mind and it makes this build particularly hard to build against. So, here's why I get what I get.

So, check this out. At level 18, Twisted Fate naturally gets 108 AD. Add a Madred's Bloodrazor and Hextech Gunblade onto this and you get 178 AD as physical damage. Now it's time to add items. Every 3 attacks, you deal an additional 42 from Wit's End and 20 from Malady plus 4% of the target's health from Madred's Bloodrazor. On that 4th attack, you deal an extra 155 damage from Stacked Deck. Now to take this into real life. At 2.5 attacks per second, this is 4 attacks every 2.9 seconds. This comes out to 592 physical damage, 403 magic damage, and 16% of the enemy's maximum health every 3 seconds.
In total, against a character with 3K HP, you deal 992 damage plus 480 to get 1472 damage in 3 seconds. You can do this for 11,250 gold in comparison to:
An AD build that costs 11,070 gold that includes Infinity Edge, Bloodthirster, Phantom Dancer, and Berserker's Greaves that deals 280 attack damage at 1.5 attacks per second plus 385 damage to account for critical strikes to deal 1135 damage every 3 seconds (assuming you have max stacks on Bloodthirster).
A Hybrid Build that costs 11,350 gold that includes a Trinity Force, Guinsoo's Rageblade, Berserker's Greaves, Hextech Gunblade, and a Doran's Blade that deals 331 damage every 1.35 second to equal 690 damage plus 300 damage from your Hextech Gunblade active every 3 seconds (assuming you already have max stacks on Guinsoo's Rageblade and the proc from Trinity Force)
An AP build costing 11,250 gold and consisting of Doran's Ring, Sorcerer's Shoes, Rabadon's Deathcap, Lich Bane, and Void Staff that will give you 397 AP and contribute 158 damage to your Stacked Deck and Pick A Card and 258 damage to your Wild Cards; allowing for a burst of 1032 damage over 3 seconds (This involves getting 4 attacks to proc Stacked Deck)
So overall, compared to all of the other builds, it's cost comparable and deals out more damage quicker; all while getting the more important items in your build quicker than you could in any of the other options commonly available.

Greater Mark of Magic Penetration- This is to get more of the on-hit effects to penetrate through magic resistance. Remember, this build gets max attack speed, but primarily deals magic damage.

Greater Seal of Attack Speed- This is to give extremely high attack speed early game and proc Stacked Deck more often before you get your first Recurve Bow. Greater Seal of Armor or Greater Seal of Health are also useful for this slot, but attack speed gives you a pretty decent nuke at level 1 but drops off about mid way through the game due to item selection. So really, it's all a matter of preference.

Greater Glyph of Magic Resist- Once again, a personal preference. Greater Glyph of Cooldown Reduction, Greater Glyph of Attack Speed, or Greater Glyph of Desolation could also be used here. I like having a little bit of fallback against magic attacks though since that's primarily what you're going to get pestered with in the early game.

Greater Quintessence of Attack Speed- This is to finish up the early game advantage you can garner from the meta. Once again, a personal choice. Greater Quintessence of Health or Greater Quintessence of Desolation are also viable options. Greater Quintessence of Armor or Greater Quintessence of Magic Resist can be used for a more resilient build.

This is WAY off the beaten path of normal game style. However, with a mix of AD and AP damage in this build, Twisted Fate benefits from both armor and magic penetration from Arcane Knowledge and Weapon Expertise . This combined with the extra crit chance from and damage from Deadliness and Lethality adds even more to your DPS. Havoc and Executioner make you extremely dangerous and potent with super ganks from Destiny.
This is based purely off of personal playstyle and an effort to turn Twisted Fate into a gatling gun with tons of damage.

I take:
Exhaust- This is a great multipurpose spell. It can turn the tide to make that 1v1 duel easier or can slow enough to ensure that you can get away.
Flash- This is a good getaway spell; which is pretty much essential since Twisted Fate is a very squishy character that lacks an escape tool other than Gold Card from Pick A Card.

Other cool spells:
Ignite- For a little bit of extra DPS
Teleport- The reduced range on Destiny makes this a much more viable spell for Twisted Fate than it was previously.
Cleanse- For when you're uncomfortable with how squishy you are and feel like you need a hard counter to CC.

Dagger and a Health Potion- With a Dagger to start, combined with your masteries, runes, and Stacked Deck, you start the game with .905 attacks per second. This give you high damage output from the beginning, makes last hitting a breeze, and gives you a nuke every 4 hits. This lets you just count 1,2,3 on minions, then walk over and attack the enemy target once and drop their health by a significant amount.

Boots- I choose Berserker's Greaves more often than any other boot type. However, if you're having a hard time staying alive or if you're getting the brunt of the enemy's CC, then get Mercury's Treads. Or, if you plan on spending most of your time ganking; Boots of Swiftness can be used to get in between lanes quicker as well as help your mobility in teamfights.

Pickaxe- This is to give you a little bit of AD for the transitional phases. This build gives you a lot of DPS, however a lot of it is reliant on on-hit effects. So before you get there, you're building a lot of attack speed, which is useless unless you have some form of damage to back it up; and this does the trick for the time being as well as building into your Madred's Bloodrazor later.

Wit's End- This is your first real investment. This in effect, gives Twisted Fate durability, attack speed, and an equivalent basic attack bonus to B. F. Sword. There isn't another item that gives all of these things that Twisted Fate so sorely needs; nor is there a way to get all of these so cheaply.

Malady- In comparison, this doesn't give near the attack potential per gold that a lot of other items have. However, it does give you another 20, increase your attack speed, and even more importantly and often overlooked, lowers the enemy magic resistance by 24. This is super important since MR is so often used to counter a lot of magic damage. This build does a good job of going around this by also building up high attack speed and a bit of AD, but in the end, the high DPS characteristic of Twisted Fate comes from magic.

Madred's Bloodrazor- This is one of the best on-hit items in the game and it will dramatically increase your damage output as well as bring you up to par and even beyond of the more dominant bruisers like Jax or Olaf.

Hextech Gunblade- This recently got a pretty big nerf, but it's still useful in that it gives you both AD and AP, which benefit your basic attack damage as well as your abilities (and it still does give a LOT of AP). It also gives you both lifesteal, and spell vamp. This means that your basic attacks heal you for both your AD damage, and your on-hit damage. Which comes out to a 35% heal overall.

Note* Depending on how durable the enemy team is building, it sometimes works better to build the Madred's Bloodrazor before working on your Malady.

Sword of the Divine- This gives you another addition to your 4 attack nuke as well as the highest attack speed rate of any item in the game. It also gives you an active that makes you even more devastating to tanks and lets you effectively counter Teemo, Jax, or any other character who enjoys building dodge.

Guardian Angel- This gives you a lot of bonuses to your defense as well as makes you last twice as long in teamfights; which is really dangerous to the other team.

Bloodthirster- This has the potential to give you the highest boost to AD in the game as well as make Twisted Fate a juggernaut in teamfights or 1v1.

Will of the Ancients- This increases the effects of your abilities as well as gives you a ton of spell vamp; which synchronizes well with your on-hit effects.

So, in conclusion, this build gives an on-hit build combined with a decent amount of AD, and delivered at max attack speed. This allows for an almost hybrid effect of keeping the enemy team from effectively building against you as well as giving a massive amount of DPS against squishies, bruisers, and tanks alike; and all for the price of the generally accepted crit/AD, AP, or Hybrid builds.