Hello, I'm a humble Teemo player who wants to tell you some features of how to play teemo ADC. I'm playing from season 1 and maining Teemo from the second season.
This guide is devoted to people who wants to play teemo adc ranked (I'm only a silver 4 now, but that was not always so) or just to have fun.
I'm making this guide because I couldn't find one which would satisfy me. Because Teemo ADC mechanics is not similar to most of ADCes.

+ Makes great Ambushes
+ Has Auto Attackers control Blinding Dart
+ Moves faster than any ADC
+ Has bonus magic damage on hit Toxic Shot
+ Good map controll with Noxious Trap
+ Difficult to counter
+ Exelent pusher
+ Unexpectable pick in ranked

- Squishy
- No escapes
- Easy beated with crowd controlls
- Hard to master
- Global taunt
- Badly depends on support
- Your teammates might not like your ADC choice

For runes take those you usually take for an ADC I can't advise something universal - it's up to you to decide. For example you can take:
Greater Mark of Attack Speed, Greater Seal of Scaling Armor, Greater Glyph of Scaling Magic Resist and Greater Quintessence of Movement Speed.
I think that that's not the most important part of the build.

For now I'm playing on a new account and I have only Teemo top runes which are:
Greater Mark of Magic Penetration, Greater Seal of Scaling Ability Power, Greater Glyph of Magic Penetration, Greater Quintessence of Scaling Ability Power. And that works! You should remember that Teemo is an AP champion, no matter if you build him ADC. After game I often see that my magic damage is even more than my physical damage even if i build him ADC or full AD.

But I don't recomend you to get sustain runes exept on seals and glyphs on armor and mr like Greater Quintessence of Health or Greater Mark of Armor and so on, despite the fact that Teemo is squishy. We are solving this problem in a different way.

As for the masteries I take 18/12/0 or 18/0/12 with Fervor of Battle . I guess bonus damage on hit, especially for Teemo with his Toxic Shot, is much better than bonus lifesteal with Warlord's Bloodlust . I also take Bounty Hunter looking forward to mid and late game, but if you want you can take Battle Trance or Double Edged Sword .

As for the other mastery column you can of course take our favorite Merciless and Dangerous Game , but I recomend you to try add some points to the third column, specially if you take per level armor and mr runes. Just count: 30 mr at start + 27 at level 18 + 5% with Unyielding and + 10% when hiited + 36 a 18 level with Fearless = and here we got 102 mr at Teemo! Without a single magic resist item.

I think there is nothing special for summoners spells pick for Teemo. The same as for the other ADCes.

Flash: I guess it's an obvious choice. Teemo has no escapes and it makes sense to take flash specially for him. Moreover, It's very useful when you make ambush from a guerilla warfare. No more comments.

Ghost: Move Quick + Ghost = extremly great movement speed. If you want to take fun, take it exept heal or flash. But i don't recomend you to take it in ranked, due to the same reason - no escapes.

Heal: Heal is a nice spell for an ADC which heals your support as well and gives you some movement. It may save in critical situation and I think it's as useful for Teemo as it is useful for any other ADC.

I think the most important thing you would like to know is what ability to max first.
Some people might think that Teemo must surely max Blinding Dart first, because in that case he will just make an enemy ADC useless for 2.5 seconds. Why not?
1. Not all the ADCes are pure autoattackers. What will we do with Varuses Piercing Arrow or Corkies Missile Barrage?
2. Blinding Dart is an ability power skill. It won't make much damage when you are ADC.
3. Blind has not a short cooldown and burns your mana very much if you use it to often.

It's much better to max Toxic Shot because:
1. It helps you to farm
2. It' doen't need mana
3. it deals +50 magic damage on hit on level 9. Most of the ADCes take B. F. Sword (which gives only 40 attack damage) and Teemo just doesn't need it because he has his e, and he can buy attack speed or crit instead.

What to max at 13 lvl? It depends on the situation. If everything is fine and you have much burst to destroy the enemy ADC at this level you can put some points in Move Quick. If it's not - take some more Blinding Dart

Now let's see.
To start with:
Not doran's, though it is nice, I also took Doran's Blade with a potion earlier but, you will most definetly sell it later and I just prefer to take Cull to recieve aditional 225 gold for free. Doran's health bonus is not so significant.
If you like, you can take Boots with potions. But though Teemo have some lack of mobility at the start he just doen't need it because he must just farm well.

Early game:
Here Berserker's Greaves will be usefull to run towards your enemy or away from him. Vampiric Scepter will allow you to stay in lane as much as it needed and helps in fights a lot. Phage is a great thing to prevent your enemy from runnig away.
By the way Zeal was also very useful and I also bought it when it was a part of Trinity Force. Stinger is not the best thing to replace it. But I advise you not to split the items and sequentially build one item after the other, rather than buy part of the Trinity Force and part of the Statikk Shiv.

Core:
Some words about our item to build first - Trinity Force and some about the most popular ADC item (well as it was some years ago ;) - Infinity Edge.

Infinity: 1. Gives massive damage 2. Gives crit 3. Empowers crit I said about damage when we were speaking about skills. Why do we need +70 ad from Infinity when we already have +50 magic damage on hit from Toxic Shot? As a first item Infinities crit will often be not enough to be impressive. Remember: toxic shot doesn't crit - Teemo is not a Caitlyn, Draven, or Jhin who have empowered basic attacks. Moreover, Teemo doesn't have any AD scaling abilities. You can ask why do we even build Infinity Edge at all? As a third Item when we have crit from Statikk Shiv and some more attack speed from Trinity Force and Shiv, Infinity gives Teemo a real power.

Trinity gives us: 1. Some health (Teemo has lack of health) 2. Some damage 3. Some mana (Teemo has lack of health) 4. Nice attack speed (It's needed for Toxic Shot 5. Great cooldown reduction. 6. Speed advantage with Phage 7. Empowers our basic attacks. (Don't think if Teemo doesn't have Mystic Shot it is useless to build him Trinity. Don't forget about stacking shrooms and don't be afraid of using Move Quick just to activate Sheen's ability.

As for the second core item - Statikk Shiv
I would take Runaan's Hurricane, but at this point you don't have enough damage to use all it's 3-hit potential. And it doesn't combine with trinity well. Shiv is much better as a second item, especially because his exelent chain lightning. Very useful to farm and to make burst.

In late game:
When you get all your we have already spoken about Infinity Edge. Take it as a third item and your damage will be insane.
As the forth - take something on lifesteal. Usually, it's useful to get more health and in that case take Bloodthirster. With Trinity and this thing Teemo is not so squisy as always.
But if the enemy is tanky and if Dr. Mundo and Nautilus are too annoying take Blade of the Ruined King if there is too much cc take Mercurial Scimitar
I'm not sure about Maw of Malmortius vs AP champs, but if you like it take it after lifesteal item.
Finish it with Runaan's Hurricane in a 6-th slot. Much attack speed, crit, movement. You can also sell boots and take Guardian Angel if needed. Or Guinsoo's Rageblade for much dps with AP runes (Very unstable, not recommended ;)

At last we can speak about playstyle.
In lane be passive. It's very important to find the right moment when to attack. Farm. When you are under 6 level don't attack the opponent unless there's no enemy creeps in your lane. Be ready for both your and the enemy jungle to come. Don't spam Blinding Dart too much. Use it only if you can make an autoattack on the same champion. Don't be afraig to last hit a minion with your q if you can't kill it with an auto.

I said that Teemo is badly dependent on support. If you have such "exelnt" support like Brand, Pantheon or Malzahar it might be pretty difficult to survive. They might appear if a support was autofilled or he just thinks that Teemo ADC is a bad choice. They can take your cs, blame you, go to gank mid leaving you alone and so on. I think the best support for Teemo in lane is Braum. His passive is greatly combined with Teemo's attck speed, Braum has an exelent shield, usefull ultimate. Aslo I like Janna as a support for Teemo. Her shield and heals, her cc make much help for you to survive and to take kills. It's not always good to play with aggressive supports like Leona, because teemo is not very mobile champion at the start and he can't always follow her like Tristana or Lucian can.

Noxious Trap is your secret weapon. Keep the bushes shroomed and be ready to attack if the enemy steps into it, but don't try to get a kill in that case unless you are sure you don't die and grab a kill. Use mushrooms when fighting close. Throw them right in you enemy, or the closest creeps who make shrooms explode even if the enemy champion didn't step right into it. You can see my own shroommap for you to know where exectly to put mushrooms.

In mid game if you feel fine and have already grabed some kills you can be a bit more aggressive. But don't go solo if you aren't sure that you can't be catched. Avoid cc. Anyway it's better to stay behind your teammates. Use your global taunt but don't be too aggressive. This super ability range is the whole map ;)

In late game stay behind and don't be aggressive at all because Teemo has no escapes and is easy killed with cc if he's not enough careful.
Don't ignore your passive. guerilla warfare is an extremly great thing if it is used properly. Make traps not far from your teammates and when they engage (they - not you) - attack. In late you will 2-3 shot any squishy champ and you won't have any problems with kiting tanks.

Don't be scared. In this item I will try to explain to you where to put mushrooms. But firstly, let's see what do the dots mean.

1. Red dots show the most important mushrooms to set. Most of them are needed to give vision.
2. Yellow dots show those which you can put if you want, but they are not so necessary. The also can strongly help you in combat in lane.
3. Green dots show are situational and here are only a few of them on the map, you can invent your own places to put them.
You must not put all the mushrooms like this, because most of them would be used and you will have to put a shroom on the same place for many times. Don'y forget to put a mushroom infront of the turret, it can be useful in defence.

Little red and blue dots show from which side it's more necessary to put a mushroom - from red or from blue if you don't cross the black line, which means that you are pushing lane. If you do, put the mushrooms prioritised for the opposite team. For example if I play for the blue team I will put only 1, 2, 4, 5, 7, 8, 12, 13, 16 until you reach the black line, and than you can put shrooms into other places.

I hope you enjoy the guide and you have found something useful for you. Unfortunatelly, I can't post here any videos with this build demonstration because of some problems with recording, but I will surely update the guide after I solve this problem. If there are any questions - ask me.