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.
This isn't your typical ap teemo or ad teemo. This is a pure hybrid with a bit more burst then is usually expected out of teemo. This isn't an entirely strict build either and does give you some leeway to play this teemo how you want.
There are really only two critical needs of this teemo. Lane mid and rush the gunblade. The gunblade is a pretty hefty first item to get, but it gives you some insane burst in the early game to grab a few kills and along with exhaust is a nice second slow. Also unless you're getting a lot of gankers coming up to you in mid, use your mushrooms for farming as soon as you hit 6. You can wipe out all minions outside of the tank even early on with a well placed mushroom. If you're comfortable with mushroom farming and laning in mid you can skip to the next paragraph. You want the back row of minions to be the ones tripping your mushroom, but you want it far enough ahead so that it gets the melee minions as well. The proximity of the mushroom is a little bigger than the mushroom itself, so place it in front of the closest ranged minion and the aoe should hit all of the minions. As for laning in mid, I find it's really good to run back and forth in the area in front of the bushes closest to dragon. (so the southside of mid) For people like ashe and morde who spam their aoes trying to hit you and minions this is really annoying for them and can really lower their minion kills easily. Just keep ducking back and forth taking pot shots at them to tick your poison on them and they should try to fire their aoe's at you and not hit any of your minions.
I think the skill selection is fairly straight forward. I like going for the quick burst of blind dart in the beginning to get that last hit on a champ or to just scare them off a bit. Your poison really starts to kick in after you finish your ap items.
I choose to pick up the 21 points in offense skipping anything crit related as we won't be building any crit items to benefit from it and I pick up 9 points in defense going for extra armor and picking up the extra dodge.
The rune selection is definitely debatable, but I like it as it is. Extra dodge [from dodge seals] will definitely save your *** a lot and is real useful for running through minions to champs without taking too much damage from them or losing half your hp when laying a shroom in a huge crowd. Ability power per level glyphs is better than straight ability power in the beginning since it's not going to add that much onto your poison til later levels. The marks and quints are definitely up to yourself. I prefer going all armor pen. This build doesn't have a whole lot of attack power, but having a tonne of armor pen early game is great and later when you're attacks are blazing fast this will help them hit that little bit harder without the ad. You could also go for magic pen marks and quints if you desire since we don't take items with it and push that poison damage that little bit harder. I don't feel this is as necessary since armor tends to inflate on most champs way more than magic resist and they need to go out of their way to get a whole lot more of it.
Item build is pretty flexible as well. I used to live by doran's shield as a starting item, but the life steal from the scepter will keep regain you hp more quickly while laning and builds better into items we need so there's no wasted gold there. I always get and finish boots next. Ninja tabi for lots of phys champions and magic treads for ap champs (though I usually go tabi regardless) Even with only 1 point in move fast you're a speed freak and having boots early can help in ganks, getting close enough to get that kill, or get the hell out of dodge when you're gonna die. After that it's just finishing out the hextech gunblade. As I explained earlier this is pretty key and gives you a whole lot of burst (especially against squishies in early game) and can be a surprise to an enemy who thinks your only burst move is blind dart. Next I get stinger because our attack speed pretty much sucks up until then and aspd is really important for pushing the poison. Turn this into a nashor's tooth and you should be pretty lethal already. You can also grab the blue buff by yourself pretty easily and go to town laying down mushrooms everywhere when you're not using them to kill creeps. Next I move into sword of the divine. More attack damage and with the fast attack speed you'll start melting faces. After this you can choose your final items depending on the game. I prefer to always have last whisper as my 5th item. More aspd and extra armor pen is great for the lack of ad we have at this point. The last item is a total toss up and this changes a lot from game to game. (if it lasts this long) If you're feeling brave and haven't had much trouble getting focused or against a heavy melee team then phantom dancer is a great choice. Wit's end is great if you're up against nukers providing magic res along with burning their mana for extra damage. Frozen mallet is great if you need the hp and want an extra slow. Deathfire grasp for another nuke. The choice here is really up to you.
Lastly the summoner spells are fairly flexible too. Exhaust is must. Blinding champs for a huge amount of time coupled with your blind dart is too good to pass up. I used to swear by cleanse, but after the nerf to it I've liked teleport more. You can set up mushrooms close to the enemy base and teleport to it to backdoor a tower or just get behind the enemy team for a gank. Flash is viable too if you like that play style.
This is my first build so sorry for my walls of text. If you've played teemo a lot and haven't tried a hybrid I'd highly suggest trying this out a few times. Your burst is surprising, your shrooms are a menace, and you attack quickly enough to keep your hp up through many tough fights. PUSH THAT POISON!!!