I really love everything about Twisted Fate, but I cant seem to really do too well. I win lane once in a while but hardly ever get strong enough to carry. My win rate is around 50% with him, so not too bad, but I would really appreciate some tips.
Personally, I never try to kill my laner with twisted fate (to a degree). I try to kill OTHER people's laners. I act like a second jg just in mid. I push out the wave with Q and ult to another lane instantly making it a double or even triple gank. This gets other lanes snowballing as well as giving you either kill or assist gold. The fact I pushed out the lane earlier with Q, even if I wasn't csing all of it, makes me lose little by the time I get back (or you can even take teleport like a shen).
Another thing you can do is select your yellow card as your ult is channeling. This makes sure there isn't any "oh it started on red card" when you get into lane. If you want to keep your camera unlocked so you can see the enemy during the gank just watch your ability icon for w. It will change with the card that its on.
What Swollwonder said is correct. You're not really supposed to win your lane exactly, you're supposed to win other people's lanes for them with the TP ganks.
You should be CSing to the best of your ability until 6, and continue to do so afterwards, look at side lanes for ganks, shove your lane into the enemy tower and then TP gank a lane. Make sure you have your Yellow card selected so you don't waste any time potentially missing out on the gank while you try to select the proper card.
Also don't do it in lane, you don't want your enemy laner to either interrupt your TP, or to obliterate your health bar making you a free kill delivered to the other lane.
Edit: I took a look at your last TF game and have some additional notes.
Runes and Masteries: For your runes I'd highly suggest Magic Penetration marks, Movement Speed Quintessences (which you have), Scaling HP Seals (Can be replaced with Armor Seals in matchups against AD), and then Scaling CDR Glyphs.
I also prefer 21/0/9 for my masteries, the added mana pool on TF is nice, and Biscuits are a godsend for TF imo. On your offensive page, and this part is largely just preference, I would suggest pulling a single point from Sorcery, and the point out of Expose weakness, then put them into Butcher, and Feast. Again that's just my personal preference, but it's worth checking out to see if you like the feel of it better.
I also notice that you seem to rush Morellonomicon in a number of games, I suggest you look at Lichbane first in most cases, or at minimum pick up a sheen, it provides a lot of extra burst damage, which is what you need on your ganks. My typical build ends up as the following. 
If you like you can take Sorcerer's shoes instead of Lucidity boots and put Morellonomicon in place of Luden's Echo or Zhonya's hourglass, but I like the way that build feels much better.
You're looking to hard burst your targets into the ground whenever you pull off a TP gank, having the largest amount of damage possible to throw at them is important, and if you're doing well, they'll have some MR for you to chew through, I find the Magic Penetration Marks and Void Staff, typically provide enough penetration to chew through what I need to put out proper damage. This build combined with your Runes and Masteries puts you at 33.75% CDR at level 18, which is plenty to throw out a ton of damage in teamfights. It brings your ability cooldowns to just under 4 seconds, and your ultimate down to about 80 seconds. If you're picking up blue buffs, it rounds out your CDR to 40%, and frankly goes over a bit, but the cap is 40%, and provides you with all the mana regen that you need for longer fights. It reduces your ability cooldowns a little further, and really makes an impact.
