Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Recently, Teemo received a massive buff. I'm talking, of course, about the Astronaut Teemo skin. Astronaut Teemo is incredibly OP, and you should take advantage of him before Riot decides to nerf the skin.
Anyway, I believe the most effective build for Teemo is now AP. Teemo can now plant more mushrooms and faster than ever before, and their damage is just insane. This paired with Teemo's ability to almost 1-shot a carry with his Q, and you have one of the best assassin/harassers in the game (or at least the most fun =P).
My preference is to go Flash/Ghost, but there are multiple viable options.
Flash is one of if not thee best summoner spell. Flash gets you out of sticky situations or catches you up for last hits. It lets you both ambush and escape from ambushes. For Teemo, who's both squishy and an assassin, Flash is incredibly useful.
Ghost is similar in it's usefulness to Flash. It allows you to chase enemies down or to escape from them. While not quite as versatile, Ghost is still an excellent choice. Ghost combined with Teemo's natural speed makes you almost impossible to escape/catch.
These other summoner spells are also very useful for Teemo, though you may want to alter your Masteries to accommodate them.
Teleport is an excellent tool for ganking and backdooring. Teleport becomes a tempting choice when you throw Teemo's mushrooms into the mix. With a pseudo ward almost anywhere on the map, Teleport Teemo can show up anywhere at anytime. If you're playing with friends, have them take teleport too; the other team wont be able to keep up. If you decide to take teleport, you should take the improved teleport mastery in utility (replacing improved Flash or Ghost, whatever you replace with it.)
Ignite is an excellent offensive spell. It works well against teams with healers and plays well into Teemo's other DoT abilities. Furthermore, improved Ignite grants you bonus AP. Because if this, I would highly suggest taking the Ignite mastery in Offense. Depending on your preference, you can shift your masteries to a 21 0 9 build to support it.
Exhaust is another offensive spell. It allows Teemo to focus targets down as well as boost his usefulness in a team fight. As with Ignite, you should build your masteries into improved Exhaust, which would greatly increase its effectiveness.
I prefer to build AP Teemo 9 0 21, but this is hardly the only way to do it. Depending on your team comp., summoner spells, and personal preference, you could also build him 21 0 9. This build shows a 21 0 9 build. Overall, your Masteries are very flexible, and arguments could be made either way. I prefer 9 0 21 for the move speed and CDR (which also decreases your Mushroom charge time.)
Like Masteries, your Runes are flexible. I prefer Magic Pen Marks, Attack Speed Seals, AP Glyphs, and Health Quints.
I won't go into the skills in detail, (there are other sources for that,) but I will explain why I picked this order.
You're going to start by taking Toxic Shot, which you'll also max first. It's tempting to take Blinding Dart first, but consider this; Blinding Dart has a cooldown and a mana cost. It deals more damage and blinds, but this is a short term gain rather than a long term benefit. Teemo's greatest strength is the element of surprise: Toxic Shot is deceptively strong. Too often players will disregard Teemo's poison damage. This is a fatal error. With Toxic Shot, every single auto attack deals additional damage as well as damage over time, and with AP Teemo, that damage will add up faster than your enemy will realize. Toxic Shot lets you farm better and harass longer, and late game you'll be able to kill people with just a few auto attacks.
That said, Blinding Dart is still an incredibly vital ability. Early game, Blinding Dart can be used to keep DPS's off of you and to harass squishys. Late game, it becomes a single target nuke and your most deadly of weapons. Even though you max it relatively late, it stays relevant throughout the game.
Move Quick is a pretty weak ability I must say. Not that its useless, Teemo definitely benefits from increased mobility, but it has very few applications. There are very few occasions when you don't want to activate it right away, and once it's on it doesn't do much. Not much to say here, just try not to get hit.
While BD and TS are your bread and butter, this is your desert. Teemo's Mushrooms (or Satellites) are AP Teemo's most powerful ability. Put them everywhere. Use them to protect your jungle buffs. Use them to protect from ganks. Use them to farm creep waves. Use them to slow an enemy chasing you. Use them as teleport targets. Use them to scare enemies out of brush. Knowing where and when to use your mushrooms is the most important skill for an AP teemo to master, but once you have you'll be killing with them while you're half way across the map.
I start with a Doran's Ring and a Health Pot. On my second trip back, I buy boots and start my Mejai's Soulstealer (of just buy it if you have enough.) From this point on, you should try to kill the carry any chance you get. Teemo excelles at killing squishy targets, and you can easily snowball an early game gank into late game domination. Just make sure not to be too agressive; you're still a squishy yourself. Teemo is one of the best champions at running away, but you should still avoid rambo-ing into enemies.
Finish your Sorc. boots. Now you need to ***es your current state. If you're doing well, get Zhonya's Ring. The massive AP boost will make you that much stronger, and as a squishy, its active can be a lifesaver. If you're doing poorly, get your Nashor's Tooth and Guinsoo's Rageblade first and play defensively. Nashor's bonus attack speed makes your Toxic Shot even better, which lets you harass from relative safety. Rageblade grants similar benefits, though not as useful to AP Teemo. (Either way, you should buy all 3 items no matter the order.)