The main idea of this build is to have map pressure with decent sustain and to quickly reduce the health of your enemies. This can be played in the Top or Mid lanes depending on the enemies Champion picks

Attack Speed T.F. isn't easy to get going, but once you do, it's a lot of fun, and has potential to become a few different things.

"Only two Jokers in the deck, and I get dealt you"
-Twisted Fate, the Card Master

These build ideas are for map pressure and/or Attack Speed. Twisted Fate is usually played as an AP carry, or occasionally an ADC. But his kit has so much Utility, you can get away with a lot.
This Build revolves around Mobility, Damage with Autos, Pick a Card (W), and Stacked Deck (E). While you can easily chase, reduce health, and increase map pressure in lanes, This build will be a little more difficult to get kills with, but is perfect for setting them up (like many T.F. builds if you don't snowball).

Depending on your enemy, you can play passively, or you can try to hit a lot of Pick a Card (W)s (primarily Red since it's a fast-moving AOE)
Mid-game focus on objectives and try to stick with your tank or maybe someone who isn't doing very well since you can easily set up kills.
Late-game should have some fair sustainability with your scaling Health and Lifesteal, along with decent Damage if you can sit behind your tank and auto.
In teamfights, do your best to set up kills for your carry and try not to get caught, since you have potential "clean up" power if the enemy team tries to disengage.

In-Lane:
You're going to need Doran's blade for a little extra Damage and life steal to work with you're boosted Attack Speed.
Depending on your lane opponent, you might need boots sooner than later, but mobility is a big part of this build, so don't wait too long. Your First item should be BoRK for it's AD and AtkSpd, so Grab a Bilgewater Cutlass. A Phage should be next, so you can get Movement Speed boost, Damage and Health. Afterwards you can set up your Core

Core:
To ensure sustainability after grabbing objectives, Ganking, or simply pushing lane, you are going to need AtkSpd and lifesteal, which are two major points to this build, and is also exactly what BoRK gives you. Trinity Force is essential for any iteration of this build because of the Damage spike and other Utilities (Crit, AP for Mixed Damage, and Movement Speed)

Western Showdown:
While you won't get many kills if the enemy is grouped properly, this Mobile AtkSpd build is useful for pushing lanes and taking objectives. and it's not bad to set up kills if you have your tank to peel for you and your ADC to finish them off.
With this build you have a large amount of AtkSpd as well as 65% critical strike chance (85% if you grab an IE), so whenever you get a Stacked Deck (E), it's likely you'll have gotten 2-3 Critical strikes by then (and more if you Stun them with Yellow Card (W)).

Heavier, faster, Shuffle:
This focuses on being able to Duel with added Health and Damage, as well as have more CC power With Frozen Mallet's Slow which makes it all the easier to Hit a Gold or Red Card more often with CDR and Mana Replenishing. All with added sustainability from Lifesteal.

Go Fish:
This build makes you Squishier, But also allows for a lot of Lifesteal, so With your AtkSpd you can duel a little easier. It also gives you a little more mixed Damage, since All your Damaging abilities have AP scaling. RageBlade's Passive also has good Movement Speed to Chase down enemies or escape.

More than one kind of Deck:
The best way to get the most amount of damage with AtkSpd TF is to build some AP with your AD. All these items in question are expensive, but if you've farmed and picked up some kills, it should be easy.

Twisted Fate is a very interesting champion to learn, since he has so much utility and map presence, not to mention you can get away with building him with either AD or AP.
This build makes T.F. a team player, helping to secure kills, pushing lanes, and grabbing objectives.
I hope you've at least been entertained by this Build, and I wish Lady Luck smiles upon you on the fields of justice, Summoner!