Hey there. I decided to remake this guide, since I realised it wasn't really good. I changed the skill order, masteries, item build and even runes. Everthing, actually. This is basically the classic TF AP build, but some items may change.

For runes, it's simple. You need a good AP to harass early. You also need some magic penetration (always useful) and armor. I didn't chose flat armor because you usually don't have to fight against an AD when you're mid, unless you go and gank other lanes, which shouldn't happen before level 6.
I chose AP quintessences, but some HP may also be good since TF is very squishy. Maybe some move speed is viable too.

Not much to say here, it's really classic and I didn't invent anything.

There we go. Start with boots + 3 HP to creep, then when you back take a doran ring or two (it can go up to 3 but I think 2 is ideal). You can also take some MR if you're against champs like LeBlanc, Veigar or Kassadin.
Then take Rabadon, it provides a lot of AP and is simply a must have on any AP carry. You can also start with Sheen for a better harass with your W (especially the blue card) but I prefer Rabadon first.
When Rabadon is built, complete your boots, either Sorcerer or Mercury.
Lich Bane comes next. Start it with Sheen, as I said it's a good harass tool. Once you have your Lich Bane, your blue card is simply awesome, but don't forget to use it with your E.
After this, take a void staff, it's not really expansive and provides a good magic penetration.
For your defensive item, as usual, take a Banshee if the enemy AP is too dangerous, and if the AD annoys you take a Zonia.
At this point I have to say I don't really know what to take. Some would take Rylai, but WotA is good for spell vamp, you gain a lot of HP when you use your Q on a minion wave. Nashor's Tooth can also be useful for the CDR and the AS, which allows you to use your E more often. It also provides some AP.

This is the build I usually take. To be honest, since I'm not a really, really good farmer, I don't usually go further than Void Staff. Only once in ranked I had the opportunity to finish my build with Banshee and WotA. But this build works as long as you're good at positionning in Team Fights.

As for gameplay, until you have your ulti, just creep with auto attacks and harass with your Q. Take the blue buff when the jungler gives it to you, but you can restore your mana with your blue card. Blue card is also an interesting tool to creep, thanks to the bonus magic damage.
I personally don't try to kill the enemy mid until I do some good damage with Q, and I wait until his health is low enough to flash + stun + Q (and E). They never see this coming, even if it's obvious. Ignite and auto-attack him if he is not dead yet.
If you have the blue buff, the red card is also interesting since it provides you a bonus range (when the enemy stays behind his minions, hit one of them and the AoE should hit him aswell). The red card's slow allows you to place more easily your Q.
Once you have your ulti, try to gank bot when they push. I think bot is more easily gankable because your AD carry and support can help you, and top is usually pretty tanky.
You really start to be a threat when you have your Lich Bane. Observe the map. Whenever an ally fights with an enemy, ult + stun and you get an easy kill (try not to ks, do this when your ally won't make it). This is something I like with TF, his ability to get kills on every lane, and the enemy mid can't do anything against that.
In team fights, you MUST stay behind your allies and harass with Q. Once the enemy is hit by 3 or 4 Qs your team has a great advantage for the incoming TF if no one engaged yet. Whenever you can, stun + Q one of the carries if he's misplaced. Also take care of champions like Talon who can kill you in one burst and get away with his ulti. You'll have to count on your allies not to let him go on you.
When the Team Fight ends, try to ult to a running enemy and finish him, it's another easy kill and people usually don't see it coming (depending on where you teleport).
Most importantly, keep farming. Q + red card grant you a quick farm.