Hey there, I'm Shardath, and this is my guide to how to play Teemo with focus on AP on toplane.
It is also my very first guide... so please vote gently. ;]

Let's be honest: You are probably here because you are pretty new to Teemo and you look for an easy way to play him. And this is what I will give to you: A build that helps you to easily get a good rating without having to be a pro!
I am not the most skilled player in the world yet this build here makes me pretty much always look good at the end of the match, even if everyone else in my team failed horribly. And I am sure it can do the same thing to you.

I realize that a lot of people play Teemo with a focus on attackspeed because it works together greatly with your E. However, there are enough good guides for that already and believe me - the way of playing with this guide is equally strong - maybe even better depending on who is playing. And I also like to think it's easier and more save.

Before you judge please go try it for yourself!
And now lets get started...

Pros:

+ Strong poking
+ Hard to gank
+ High movementspeed
+ Easy lasthitting
+ Deactivation of the enemy ADC through blinding
+ Map awareness through shrooms
+ Sometimes winning teamfights before they have even started
+ So much fun.

Cons:

- Squishy
- Often focused
- Shrooms can be countered by Oracle's Elixir and Vision Ward

Quintessences:

3x Greater Quintessence of Movement Speed helps escaping from ganks a lot
or
3x Greater Quintessence of Ability Power for more early damage/easier lasthitting.

Glyphs:

9x Greater Glyph of Scaling Magic Resist will help a lot to compensate for squishyness
or
9x Greater Glyph of Ability Power for more early damage/easier lasthitting.

Seals:

9x Greater Seal of Armor
If you go top you will need these.

Marks:

9x Greater Mark of Magic Penetration
Magic penetration increases your damage output a lot, especially early. Anyone who deals magic damage should pretty much always take these.

Flash

Flash. Everyone picks it, always. It helps you to escape, it helps you to chase, it helps you to land that one last autohit/Q that secures the kill. It is metagame for a reason. Take it with you.

Recommended:

Ignite

Through our masteries, Ignite increases your AP and AD by 5 which is pretty nice early. But more importantly it helps you to finish off an enemy after you poked him or her a lot. Since poking is what Teemo is best at, this is what I recommend.

This one is pretty nice, too:

Exhaust

Exhaust also helps you to kill the enemy on your lane. Your W will help you to get close enough, then you just unload. (Enemies with good escape mechanisms that do not depend on movement speed will get away anyway, though.)
And it helps with escaping, even though you already got your W and flash.

Basically, ignite is better for enemies who can just jump away when you exhaust them. Else exhaust would probably be a better option. On the other hand, ignite gives you a nice bonus on AP and AD for early laning, which is why I'd recommend it since you can make use of both. But if you personally prefer exhaust that is totally fine, too.

Other stuff we should talk about for a moment:

Teleport

A Teemo with this spell has the advantage of being able to teleport to your shrooms. Lets say an enemy champion runs into one of your shrooms in the enemy jungle. You can teleport to another shroom close, then finish the already weakened enemy off, then run away since you are good at it. If you plan on doing that: Ok, cool, why not? It also helps you to defend other lanes in trouble or quickly join unexpected teamfights.

Ghost

If you pick both Ghost and Flash you are barely gankable. And you don't pay a very high price for it since it also helps with chasing. It is very usefull - but I don't recommend it. Basically with your W you already got a small ghost-skill with a much lower cooldown. You won't really need this unless things go really, really bad for some reason.

Passive - Camouflage

First of all lets talk about Camouflage. Stand around for 2 seconds - which can be VERY LONG two seconds! - and you go invisible. As soon as you do anything, you become visible again and gain a nice boost on your attackspeed.
This ability has two main uses: Ambushing and hiding.
The problem with your stealth is that you need to stand still. So when you are suddenly gone after being chased into a bush, the enemy will usually know where you stand and just fire skillshots at you. Running away is usually smarter. However, if the enemy didn't see you in the first place, this can still save your life.
But the better way to use this ability is to set up an Ambush. Put a Shroom into what I call a "high traffic area" - more about that later - and wait for someone to run into it while savely in stealth. He will be slowed, take a lot of damage through your shroom and since you got the attack speed bonus he is all yours. And if things don't go as planned - if the enemy is not alone - then you just stand still.
Important: Press S to cancel auto-attacking!
You will often have to do that in order to keep Teemo from going out of stealth unplanned.

Q - Blinding Dart

Your personal carry deactivator. Blinds the enemy so his normal attacks miss for up to 2,5 secs.
Remember: Just the normal attacks, abilities still hit!
It also scales nicely with AP and will become a very usefull tool to deal a lot of damage later.
We max it last - it's not a bad ability, but poking with your E is more effective because of the mana-costs of this ability and your W helps you with escaping more then this here does.
Protip: Keep the enemy from lasthitting the big minions by blinding him in the right moment.

Situational possibility:
If you fight against someone who relies on auto-attacks a lot you should max this first. Same goes for when the enemy jungler is screwed when blinded.
For example if you play against another Teemo while Xin Zhao is the enemy jungler it is obvious that you should max Q first. But the most top champs - like Darius, Garen, Singed, Nasus - are melee and can't poke back while they are much less squishy so your E is the better choice.

W - Move Quick

It's like Ghost - but with a passive bonus, lower cooldown and lower duration. It will save your *** so many times, helps you to get around the map faster and helps you to chase the enemy. It's just so, so usefull. Which is why we max it second before our Q.

E - Toxic Shot

This ability gives a huge boost to your auto-attacks and is the main reason why you should not play Teemo AD. It scales with AP for 30% + 10% for the DoT and it is much easier to achieve high amounts of AP then to do the same with AD. It helps you a lot with lasthitting early game and is such a powerfull poke. We max it first.

R - Noxious Trap

This is why you are here. These are the famous SHROOMS OF DOOM.
They are awesome in so many ways. First of all they help you a lot to prevent and/or escape ganks.
Then they deal a lot of damage when combined with the right items. People without MR are half dead before the teamfight even started. And also they help you to clear waves of minions in high-speed.
But more importantly they give you one of the most important things in the game - map awareness.
Your shrooms are like wards on mass-production with the potential to really hurt the revealed enemy. If someone sneaky is busted by a shroom and a teammate is nearby your assist-count will usually go up by one. If you do your job right the enemy won't dare to enter their jungle anymore - which gives your team a huge amount of control over the map. And this, my friend, can and will make the difference between success or failure!
There are only two things you need to worry about with your shrooms...

There are three types of areas where to put your shrooms and where to find them on the map:

High Traffic Areas
HTAs are areas where the enemy is extremely likely to cross and pop your shroom. You should always put your shrooms here as soon as you got Liandry's Torment. They will weaken the enemy a lot. They are also the typical spots for your enemy group to go when they attack your base, depending on which team you are on.

The circled shrooms are what I call the "golden three".
Always put them down.
You will not regret it.

Map Control Areas
These are the entrances to the jungle. Putting your shrooms here means you can keep teammates from unexpectedly being ganked. Place them in these areas when your team is going into defense.

Shrooming baron and dragon is not a bad idea but usually it's the job of the support to ward these.

Yellow dots with a red dot in the center have higher priority.

Gank Protection Areas
You guessed right. Put your shrooms here to defend yourself from being ganked. It's not just about revealing the ganker in time - it's also about slowing him when he is jumping on you. Putting a shroom close to your tower can also be very helpfull if the enemy is getting cocky.

So check out this map here to figure out when to put your shrooms where:

This map is for when you go top, of course.
If you go bot, shrooms in the lane-bushes become even more helpfull.
Remember: Shroom placement is situational. Think before you plant them.

There are two ways to seriously counter your shrooms:

Vision Ward

Sometimes the enemy on your lane or the supporter in mid-/lategame will be smart enough to put these down. The most effective way to deal with them early is counter-counter-warding.
Put your own VW down, destroy the one of the enemy. Has the nice side-effect of revieling enemy stealth-gankers and counter-warding your lane so that you are protected from ganks while your jungler can come and gank without being busted. And if they want to prevent that they need to buy another VW.
In mid-/lategame you might want to buy an Oracle's Elixir to fight counterwarding or just ask your supporter to do so if he isn't already. Which he should. Unless he dies all the time. Which he shouldn't.

Oracle's Elixir

Oracle's has one big problem: It doesn't work for stuff hidden in bushes. Most of your shrooms can not be countered with it. If someone buys it he is likely to run around by himself in order to search for wards. This is your chance: Just wait until he runs into a shroom in a bush (by using your passive), then finish him.

This guide is written with a focus on top-lane. However, Teemo can play everywhere. Yes, apparently even jungle.

Top
Usually we of course prefer top. Thats because many top champs are melee. You are ranged. That is a big advantage, especially when paired with your great escape mechanisms. Most champs will have some kind of skill that attempts to counter this. Try to provoke them to use these in a wrong moment, then strike while they are on cooldown!

Bot/"ADC"
If you got a bro who plays Blitz, Nami or Taric drag him into voicechat with you (because timing is SO important) and go bot together. The results are awesome. Stun (or my personal favorite: pull), then shroom.
However, since botlane is all about teamwork with your partner I do not recommend going there with randoms. You will have to lie before the match to keep people from *****ing: You say you go ADC when in reality you build AP - while still going bot. And if your supporter gets pissed at you because of that - even though it works perfectly fine - your teamwork is practically dead. Do not underestimate psychological stuff like that: He will have no trust in you and play way too defensive. What you want is batsh*t crazy offensive with great timing.
Yes, by doing this you will have a little bit too much AP on your team, especially if top and/or jungler too are AP but my personal experience is that the enemy won't react too much (=stack MD), especially not in normal games.

Mid
Mid is just dangerous. First of all almost all your enemies will be ranged. Yes, thats also the case at bot, but there you can make up for that with how great shrooms and stuns/pulls work together. Here you are alone - against ranged champions with many abilities with focus on haressment. You do, however, have an advantage against skillshots because of your movementspeed. Ziggs, for example, won't have fun trying to hit you. So if you play against someone like that mid might be a good idea.

Jungle

I highly respect the art of trolling - especially if you still are credit to team while doing it. But this is not a troll guide. Stop stealing Shacos job, man. I mean just look at him. He clearly has seen enough of all that "trolling" at the cost of HIS jungle and HIS art.

Note at this point: Shacos boxes + your shrooms = fun.

Start with...

... Boots and 3x Health Potion to play it save.

Movement speed helps you to dodge skillshots, pots give you a lot of sustain.

... Amplifying Tome and 1x Health Potion to play offensive.

Lasthitting will be easier, poking stronger.

Boots:

Sorcerer's Shoes + Enchantment: Alacrity

Magic pen. Standart pick for every AP-user. Makes your skills hurt much more, especially early - even if you didn't buy an AP-item yet!
The movementspeed-enchantment is pretty nice for Teemo. Your W makes it more effective and it helps you a lot to escape and chase.

Your first big item to buy:

Liandry's Torment

Dear Liandry's Torment,
i love you. Because of you my shrooms hurt so, so bad. Every time their DoT ticks, you refresh yours and tick too. And since they slow the enemy you deal double damage. As if that is not awesome enough, you give me magic pen and a nice amount of AP which helps my other abilities, too. And you give me more HP so I am less squishy. All that while you still cost under 3000g and your buildup Haunting Guise is an awesome item, too. You just are exactly what I need. Please marry me.

Love,
Teemo.

Your second big item to buy...

...if everything goes well:

Athene's Unholy Grail

If Liandry's Torment is your wife, Athene's unholy grail is your affair you just can't resist. Long story short this item is an blue-buff with magic resist and AP on top of it which only costs 2600. Do I have to say more to convince you? Well, since we play with an focus on AP, we want to put down as many shrooms as possible. So we want CDR. But shrooms cost mana so we also need mana regen. And while we are at it we have to also become less squishy. Since you can run away, AP-nukes are more problematic then enemy autohits or close-ranged abilities. So we want MR more then armor. And this item provides us with ALL OF IT.

If there is the rare situation where you always get the blue buff because noone else needs it you may buy Nashor's Tooth if you really want to and if the game just goes perfect so far.

...if you need to play more defensive:

Rylai's Crystal Scepter

Rylai's slow works great in addition to Liandry's passive. Now your Q also deals double damage with Liandry's while it also helps you to escape tricky situations even more. You also get a lot of HP to survive longer and a nice amount of AP so you don't fall behind with your damage. Only problem is that it doesn't give you MR. But if you picked the MR-per-level runes you should be fine anyway.

Your third big item to buy...

...if you picked up Athene's:

Nashor's Tooth

Every Teemo-player loves it. First of all it will raise your CDR to the max - now you can put your shrooms everywhere. Then it gives you more AP which is important to keep up the nice damage. And then it gives you something very usefull: Attack damage. Basically this is increasing the damage per second of your E by ~50% (roughly since there still is your DoT). Since you are being focused most of the time you don't really have the time do just stand around and auto-attack in teamfights. But if you do this will help a lot. It also makes you a lot more deadly in 1v1-situations.

...if you picked up Rylai's if your game has recovered:

Athene's Unholy Grail

...if you picked up Rylai's and sh*t is still hitting the fan:

Banshee's Veil

I pick this one if everything is going straight down the toilet - when I can't afford to buy anything but a lot more defensive power at this point. The passive protects you from many nasty things: Blitzcranks pull, Tarics stun with it's outra(n)geous range, Thresh's chain, Nidas spear and much more. Then it also gives you HP and MR. It is situational, but it's an situation you will encounter sometimes no matter how good you are - because sometimes your team just sucks.

Your fourth item to buy:

("Wait, the game is not over yet?")

"Yeah, but I'm doing pretty well."

Rabadon's Deathcap

Time to increase the AP of all your items - including this one - by 30%! Now you are a monster, your shrooms a nightmare. You should be winning now. One shroom nicely popped by the entire enemy team at once - probably balling at one of the golden threes - and they are done for.

"Don't ask, man. This game is a nightmare."

Guardian Angel

If things really go that bad you need some armor now. More MR doesn't hurt eather. But most importantly you should trade one of your green shrooms with one of Super Mario's. At least once every 5 minutes. Be revived when you die, get a second chance to place one nice shroom in the middle of the fight; maybe you can turn it around. Yes, your damage is solely relying on Liandry's and the AP of Rylai's now, but there are worse items to rely on and your shrooms still slow the sh*t out of the enemy.

Last big item to buy

Runaan's Hurricane

Okay, so it's one of these ">60 minutes"-games. Enough of this cr*p, time to melt the enemy away in the next (and last) teamfight. First of all you get +70% attackspeed now. Damn, that's a lot. And second you now hit three targets at once, applying your E to every single one of them. The only reason we didn't buy this earlier is because like I said, you get focused a lot so you can't rely on autoattacks that much. However by now your whole team will have a finished build and they won't be so sure who's the most dangerous member of it. Make use of that: They either put you on top of that list or they lose. Simple as that. And if they now focus you you can still just run away.

(...and if the game went so bad that you are still forced to buy defensive items then you probably lost anyway unless someone else in your team is f*cking Son Goku in person or something - which is probably why this game could last this one in the first place. If that guy is playing AP, buy Abyssal Mask, if not just buy Warmorgs or something.)



Let me say something about my build:
It is unconventional. But I promise you it works. If I would just pick Malady, Nashors, Hurricane and so on as first picks then I wouldn't have to write this guide because enough other guys are already having that build. This build here has a main focus on making your shrooms hurt a lot and on you being able to put a lot of them down without going OOM. It sure as hell is not meta - but that means it also sure as hell is not the reason why so many people lately are claiming that Teemo is useless. With this build here he is not. Trust me. Try it.

Item picks are always situational - at least to an extend. Sometimes it's smaller, sometimes it's bigger. I am not saying that these items are foolproof picks for any situation. Just for the most of them. Items like Thornmail are still out there. And sometimes you will have to pick them.

And like I said: I am not a pro. I still make a lot of mistakes. Yet this is what I get!

(If you want to you can send your own pic of your game history to me. I'll put it in here, too!)

Thank you very much for reading my guide. I have put a lot of thought, love and Teemo-experience in it so I really hope that it will help you a lot.
If it does: Vote up!
If not: Tell me what went wrong when you tried it!
Please be fair and don't downvote without trying it.

It was fun writing it. Again: Thanks for checking it out and have a nice day!

Before 03/18/13
All kinds of early fixes. You know, grammar, a few extra sentences...
The usual stuff you notice right after publishing your guide.

03/18/13
Added "F*ck the meta: It works!" for game history.
Added "Where do I go?" for choosing your lane.