DISCLAIMER/READ THIS **** RIGHT HERE BEFORE THE REST OF THE GUIDE-I am currently a level 26 pubber who enjoys TF. If you want to, you may let you cloud your judgement. However, keep this in mind, because I have limited experience and probably make stupid mistakes in itemization, runes, and masteries. These are what have worked for me so far, but if you think you have a better rune/mastery build (which you probably do because I don't have full sets of either), go ahead and tell me and I'll take it into account.
ANOTHER DISCLAIMER-For some people, this guide might not be for you, and that's fine, you don't have to like hybrid TF. In that case, go ahead and downvote, I won't mind. But give me constructive criticism so I can make this better (besides "hybrid is dumb go ap/ad". Hybrid guide hurr). I'm not putting this here because I know it's the best thing ever and your opinion is irrelevant to my feelings, I'm putting it here so you can enjoy and try to rape face with my, good for me, build.

Too many a time, I see people arguing amongst themselves. "TF should be AP! No, AD, AP sucks lategame! On hit/as is the ****! That only works for 2 levels lol, go pub somewhere else noob."

It's honestly hilarious how people like this ignore how, IMO, TF should be played. He has a long-ranged slow-moving, at least, relatively, skillshot with meh damage and meh AP ratios. He has a variable mana restore, aoe damage and slow, or stun, with, again, meh ratios, but very spammable. Then he has a passive aspeed (for AD), and CDR (for AP) increasing skill that causes his attacks to deal damage every fourth hit, with respectable ratios.

However! What doesn't make sense is that AD can't use the ratios on his other skills at all, but AP is even squishier and needs to attack to deal AP output, with additional damage that could be provided by AD ignored! So, the only reasonable solution is to combine the two, but nobody seems to pay attention. I mean, looking at his skills, he seems to be built for hybrid. Everything about him just screams "HYBRID OOH LOOK AT ME I'M A HYBRID".

Pros
Deals insane damage
Great at farming and helping the team farm
Incredible ganker, able to be everywhere at once
Ridiculously good lane sustain with Blue Card
Good lane harassment and poking
Good split pusher
Cons
Squishee as ****
Less range then standard AD carries
Liable to get focused early
No natural escape mechanisms besides Ulti, which shouldn't be used to escape
Underplayed

I don't have a full set of runes (still level 10-20 runes ftw), so this is my "theoretical" rune page for TF, once I get it finished.

Same with masteries, although I don't really know what's best for TF, I know one complaint is that he's very squishee. Therefore, I take some talents in the defense tree to make him less squishee. The rest of my points go into offense, and for those who want to know, you should never take CDR masteries or runes for TF, because if you get a Nashor's Tooth (and you will), you'll have 40% CDR just like that.

In lieu of a properly formatted item section, I'll go with my choices and why I pick them.
These do not need to be built in the order provided. This is, however, the order I usually have them finished in.

Berserker's Greaves-Provides more Aspeed to proc your Stacked Deck more. Alternate choices are Mercury's Treads (if the enemy team is full of hard CC), Sorcerer's Shoes (if they're MRes tanky, that'll block a good bit of your damage), or Boots of Swiftness (if you're bored). Under any circumstances, NEVER EVER EVER get Ionian Boots of Lucidity. Your Nashor's Tooth will be all you ever need.
Guinsoo's Rageblade-An excellent choice for TF, providing an excellent amount of AP and AD for its cost (at 8 stacks = most cost effective item in the game, fyi). The passive is incredibly useful as well, and is the main selling point of the item besides its general cheapness. Since you will be able to spam spells and attack like a **********er, you will generally have 8 stacks in short order, if not being able to keep it up permanently. Tasty aspeed is tasty.
Nashor's Tooth-Rush this ****. The 25% CDR by itself is a deal maker, bringing your CDR to 40% with one item, no runes, no masteries. But besides that there is that incredibly delicious amount of Aspeed, as well as a good amount of AP too, for your pleasure.
Malady-Another incredibly useful item for it's nice amount of attack speed and AP. The passive is another selling point, causing both a good amount of extra pain, and shredding mres. The -24 mres will cause your Pick A Card and Stacked Deck to do that much more damage, and it shows. Consider replacing with a Wit's Endif faced with heavy magic damage/burst.
Hextech Gunblade-One of your most coveted items evar. Besides providing a very nice amount of AD and AP, it has the added bonus of LIFESTEAL/SPELLVAMP FTW. Once you get this, health sustain won't be a problem until you get focused (and mana sustain never was a problem). Also, the active should never be forgotten. It has respectable range, is another nifty nuke, and has a good slow attached. Use it on fleeing enemies to make them rage.
Trinity Force-If the game isn't over by now, it might as well be. Once you have this, you can destroy their other team utterly because your 3.6 second cooldowns allow the sheen effect to be spammable pretty much on command. Also grants rediculous synergy with your Pick a Card. ALSO, I always get the Sheen component immediately after I get my boots/nashor's tooth depending on how good I'm farming. Sheen will cause your burst to skyrocket, and the earlier you get it, the less you have to work for it later.

I usually get Ghost and Surge as my summoner spells, for good reasons. While Exhaust nowadays is just used, by what i've seen, to catch a person and escape from a person, Ghost is so much more useful than that. By more useful, I mean it provides basically the same bonuses, i.e used to catch up or get away from someone, but works on yourself, making it more useful at/against groups.

Surge is new, but I tried it and now I love it. No Hybrid should go without it, especially TF. Reason being is that TF benefits so greatly from the Aspeed and AP, he (would like someone to test with full runes, masteries, and items, and get back to me) can easily become Aspeed capped from this and cause his Stacked Deck, Pick a Card, and **** throw to deal soooooo much more burst. It's insane, really.

First, Loaded Dice. Loaded Dice is so incredibly useful that it's... incredibly useful and awesome. Mainly, it'll allow you to farm better (last hit every creep in your lane and that's 12 extra gold. Not a lot at first, but over time, that's a lot.). Also, once you get lategame and can generally decimate waves of enemies within seconds and 2 shot jungle creeps, this will help you so much it's insane. Clearing the entire jungle, not including dragon or baron, will net you 30 extra gold, doubled if you take the enemy's jungle. Again, not much, but it adds up. Also, it helps your allies farm, but that's for a different guide.

I start with Stacked Deck and max that first so I can get the 15% CDR asap, and because the damage, once added on to your attack damage, is quite considerable early game. I use it early game to harass by hitting creeps 3 times, then going for a poke. Be careful when doing this, btw.

Alternating in between levels of Stacked Deck is Pick A Card. It provides, in order, an incredibly high damaging poke that also restores mana (spam this a lot), an AoE slow and damage that is useful for clearing waves, and a stun that adds a meh amount of damage. This stun is hilarious because if you have maxed attack speed and you stun them, that's 6 free hits, which will generally kill anything. Try to time these with Stacked Deck procs, and rushing a sheen will cause this ability's damage to rediculous levels. 3.6 second cooldown at 40% CDR.

Wild Cards... I don't really use this skill, to be perfectly honest. It does have a short cooldown and is spammable (3.6 at 40% CDR), but it's a slow skillshot. The only saving grace, IMO, is it's long range and the fact that it does do a surprising amount of damage (even though the ratio is meh). Surprising meaning that most people expect this skill to do jack all, when instead, it does about 2 bars more then jack all. I level this last and use it to spam in team fights, proc sheen, and finish off fleeing people.

Destiny/Gate is awesome. Yes, it's not global range any more, but it doesn't need to be. At 72 seconds CD (you do have that nashor's tooth, right?), you can just be ****ing everywhere and generally wig people out. Also, it pops banshees, which doesnt make the person revealed, but now their banshee isn't up, so that's nice. Level this when you can, as almost any other ultimate.

Well, I hope you enjoyed my guide. As said before (which you should've read), constructive criticism is accepted and celebrated.