This is something of a hybrid TF build, since ti blends attack speed with AP, rather than going for straight AP. Straight AP can work, even with the recent changes to TF, but that extra attack speed is more Stacked Deck shots you throw, and more damage to turrets. This build also focuses on map control, with both teleport and Destiny/Gate being used as ways to move quickly to someplace they don't expect you to be.

Update:

I have decided to make this a living guide, where I will update strategies and different builds that I find work. For the moment I don't plan to remove any content except for tweaking the graphically listings of Items, Runes, and masteries at the top. Changes will be recorded in the Changelog below. Item and Rune changes will not be recorded because they are outlined in the rest of the guide below for the strategies I've toyed with, but Masteries aren't documented there so I will record mastery changes here as well.

Changelog

5/27/2011
Updated Items for AD build, added AD build. Moved a point from Archmage's Savvy to Alacrity since AS is more important than AP with the AD build.

I tend to go with Mag. Pen. marks, Armor per level seals, and AP per level glyphs with flat AP quints. This gives you enough magic pen from runes to cut through some of the lower level mag. resist items, while giving you decent AP growth over time and a decent chunk of it to start with. TF being as squishy as he is needs some kind of defense though, so I go with Armor per level to ward off physical attacks since they're generally more unavoidable than magic damage. Whichever defense you prefer to have in a seal is fine.

For masteries, I go with 21/0/9, speccing into Spatial accuracy for teleport and experience gain to be sure I level as fast as possible. If you fall behind with TF, it is very hard to remain a threat, so this is a must. I also choose increased health/mana regen in the first utility tier because frankly, I don't intend to die, even though it does happen. These are up to you as well, but experience gain, gold per 10, and teleport are a must.

Old Build for Magic Damage TF

To start with I go with a Dagger and a health pot. TF being squishy will sometimes live off of the things if you take a lot of damage. After that, I go for Sorcerors shoes and keep at least 1 or 2 health pots until I'm max level or run out of room. Then it goes Malady, Sword ofthe Divine, and either Madreds if the other team is getting a lot of health, or Rylai's if I'm having survivability issues. Depending on what's left I usually opt for Trinity Force and Madreds if I decided for Rylai's earlier, or Banshee's veil/Thornmail depending on what's killing me. The defensive items can be moved up the list if you're really having issues staying alive, but if that's the case it's usually because your positioning in fights isn't goo, or you've fallen behind in level.

Revised Item Build for Hybrid-ish TF

I've refined my Item build to be more focused on AD and it's been working well for me. I've swapped out the Sorcerors Shoes for Berserker Greaves and built for Madred's Bloodrazor first after that. Then I go for SotD and start building crit from there. At this point (before building crit) you should already have substantial attack speed from here and with your AP Runes your SD should still do significant damage. Combined with Madreds you already have seemingly solid AD though majority of it is actually Magic Damage. Once you start building Crit (I go for a Phantom Dancer for the Attack speed first, then Infinity Edge) you'll be doing solid actual AD in addition to the solid Magic damage. You should be able to rip tanks to shreds with these items alone. At this point the last Item I get is really dependent on the situation and what I need, be it MR I get a Banshees Veil or Quicksilver Sash (usually BV since if I get hit by CC I'll be dead before I can think to use QSS), Armor I get Thornmail, or If I want more hybrid I build a Hextech Gunblade. Games usually don't progress far enough for me to finish a build though.

AP build/Old Build

I get Pick a Card (PaC) first for the CC, and then leave it alone until the end of the game. The only thing that scales up with it is damage and mana cost, and this is not where the damage comes from in this build. Stacked Deck (SD) next, and be mindful of when your next hit is worth more. Many a TF player has jumped into a situation and died because they didn't go in with that little extra umph ready to go. Beyond that Max Wild Cards (WC) first, Putting points into Destiny/Gate when appropriate, and SD next. These two abilities are where most of your damage comes from, since you're building AP.

Revised/AD Build

I tend to go with the same skills here as above. With the AP runes your Wild Cards will still deal surprising damage to enemy champs, and give you an edge over the straight AD tf's if you ever go 1v1 in a normal game. The only real difference with the AD/hybrid-esque build and the AP/Mag. Damage build is that your auto attacks deal more damage when they don't have SD, and WC and SD do a little less for you. In return, you gain substantially more backdooring/turret wrecking power than the AP build since WC and SD don't trigger on structures.

Teleport and Flash, all the way. Teleport may seem redundant, but it's there for a good reason. Flash is a great "get out of fail free card", and a good way to catch someone you're chasing to get that Red or Gold card off.

Heal - it's a good spell, and can be a surprise to your enemies when you suddenly have more health than them, but it isn't for this build. Health pots are cheap, use them.

Rally - I don't use it. Ever. I have seen it provide an edge in a team fight, which is important, but I think there are better options out there. Let someone else have it if they want it that badly.

Cleanse - Great for removing CC, but a shadow of it's former self. If you really want this spell, then buy a Quicksilver Sash. It's better.

Clarity - With your Blue card now restoring 65% fo the damage ti deals as mana, you should almost never find yourself in a situation where you don't have enough mana for a PoC, which will get you enough mana for a WC. Let somebody else carry it if they want it.

Revive - This could be a very useful spell with TF, though since I don't intend on dying and TF is very squishy, I don't carry it. I would find myself dying, reviving, Gating back to the fight and dying again.

Exhaust - not a bad choice, but again a shadow of its former self. Only really good for its slow, which your Red card inflicts in AoE. Not worth it.

Ignite - Good for killing someone running away from...oh wait, you can just gate in front of them and continue the hurt. Nevermind.

Ghost - Good for chasing someone or running away, but again Gate is just as if not more useful for both scenarios.

Smite - Are you jungling? No? Then don't carry it with TF. I wouldn't recommend jungling with him either.

Fortify - Let the tank carry it if they want it.

Clairvoyance - Good for seeing in brushes and warning you of someone coming to gank you or a teammate, but with Destiny if you're worried enough to do something about it, you might as well reveal them all.

Old AP/Mag. Damage build

This build offers you 2 very big things. Substantial damage, and map control.

Laning Phase

Carry

If you're carrying, than focus on getting those last hits in, and punish the other carry for getting too close. If they look like they're getting ready to jump you, get a Gold or Red card ready, and try to get your SD up with it, that way you should be able to get both off on them. Use WC to harass, but be aware that spamming it will drain your mana quickly. You can devastate an entire minion wave with a Red card and a WC at later levels, so don't be afraid to rob them of their minions when you can. You will start to run low on mana, so be sure to use a Blue card on minions when you drop under half mana, because it can go quick in a fight. The CD on PaC is very short so you should be able to chain 2 or even 3 blue cards together to get yourself enough mana to survive off of. If you start to pull ahead or get some breathing room, look for somewhere in the other lanes where you could Gate to and contribute to a kill at the very least. If Gate doesn't get your team a kill, or save your life, it was wasted.

Solo laning

This applies to laning against 2 people by yourself. Your sole objective is not to die. You should out level them, so don't be afraid to hug your turret until you feel comfortable trying to take them on. If you get a kill and die, but one on their side lives, it wasn't worth it. Try to get a Gold card on one of them if they decide to try and attack your turret, and try to time it so that they eat a shot or two from the turret, but that's about it. Your WC have a pretty long range, so harassing with them works well, but always have enough mana for a PaC. Always.

Straight Laning

You want to avoid damage, but be close enough to stun the other team or punish them for misusing an ability. Being able to stay in the brush is nice so you can jump out with a Gold/Red card and follow up with WC or SD, and then fade back behind your minions. Remember to use your Blue Card to build up mana when you start to run low, and use WC to harass. Keep your eyes on the other lanes to watch for an opportunity to Gate in with a gold card ready, they will present themselves.

Team Fights

You don't want to be in a team fight. You're squishy. If you're in the middle of one, odds are very good you will die, so be mindful of your position. Don't be afraid to show up a tiny bit late to a Team Fight so that the other team is focused on your teammates. If someone starts gunning for you, either nuke them down before they can wreck you, or get out if you can't. Flash is good for this. If they can't see you anymore they will go back to the fight and forget about you. If the entire team decides you need to die, then there isn't much you can do other than toss a Red card back, Flash through a wall, and either run for your life or Gate someplace else. Remember WC do NOT scale their damage down as they pass through targets, and the two side cards have gotten me more double kills than I can count. Remember, you want to get in, and get out of team fights, not stay in until you die.

Other Useful Tips

Remember when I said you would get plenty of Map control? With Teleport and Destiny/Gate, you can damn near be in 2 different places at the same time. If you notice a minion push getting close to a tower, and you KNOW WHERE THE ENEMY TEAM IS (that's important), it's easy to be there to wreck a tower. This might mean not being in a teamfight, but odds are good that once somebody notices that you are destroying/have destroyed a tower, a DPS from their team will go back rather than try to base race with you, and that's another of their DPS that isn't in the fight anymore. More often than not, their entire team will start backing out, and if your team is giving chase, feel free to gate ahead of the other team and let loose a gold card or two, picking up some kills.

If you find yourself in a situation where you are overextended and can feel the gank closing around your neck, pop destiny and see what's coming. If you can take the one person coming at you, feel free to jump on them before they're ready to go with Gate. If you know you are about to die because they pretty much have you surrounded, Gate to another lane or even back to your fountain if you're low on health. Gate isn't just for getting kills, but for saving your *** too.

Do not be afraid to use Destiny/Gate to just jump a little bit ahead of somebody running away from you. A lot of players only use it to jump across the map, but if jumping a short distance gets you a kill you wouldn't have gotten before, then it's probably worth the jump.

Gating into brush can give you an even greater element of surprise, when enemies just walked out of a brush and know you can't possibly be there. You can also use other abilities inbetween Destiny and Gate, so make sure you get either a Gold card or Red card ready before you Gate to a fight.

My usual rotation involves Gold card, WC, then auto attacks until PaC is off CD. SD scales with AP, so even though your auto attacks might not do damage, every 4th one will hit hard, every 2nd if Sword of the Divine lined up that way. I also try to keep an Elixer of Agility on if I can afford to, since the elixers give you a solid edge in combat.

In closing, I cannot stress how important good positioning is to playing TF well. You don't want to be in fights, but just outside them shooting in, otherwise you're probably dead already.

Revised AD/Hybrid-y Build

This build plays very similarly to the other one. Since you're more focused on building AD though, you need to be more involved in Backdooring or tearing turrets down than killing champs late game. Positioning is still extremely important, maybe even more so since you don't get the survivability of Rylai's with AD. As a result, TF has a rather high skill threshold. If you are involved in a team fight or your team starts QQing because you aren't in the team fights, you should be targeting the squishies first (like always). While this doesn't maximize your Madreds damage, it hurts the opposing team much more and you can always Gate to catch a running tank when he's alone. This build plays very similar to the AP build, so there aren't many other differences to discuss. Just be aware that you have more turret wrecking potential and use it as often as possible.