Hi StnFlu here with a Mobafire Build on AP Teemo. This is my first build that I have published, and I decided to do it on Teemo, my favourite champion, he is easy to play, but hard to master.
His Blinding Dart and Poison provide your main supply of damage, these ability's provide most damage, along with shrooms. Mushrooms are your escape route, ward and kill. They can slow pursuing enemies, farm minions and kill an unsuspecting champion in through the jungle. It is what makes Teemo the "Swift Scout" he is. Move Quick is good for escaping ganks, chasing enemies and getting back into lane as quickly as possible.

Pros and Cons

PROS
-Teemo can do some serious damage with his Blinding Dart & poison
-Epic Shroom farming
-Great in team fights
-Well rounded champion
-Great at escaping ganks
-Easy to play
-Amazing passive that makes it easy to hide
-One of the fastest champions in the league
-Basically free wards (shrooms)

CONS
-Super squishy
-Compared to other ranged champions Teemo has quite a small range
-Vision wards and Oracle's elixir can shut you down
-Usually focused in team fights
-Needed to be played carefully early game due to squishiness

Let's take a look at Teemo's four skills and passive.

CamouflagePassive: Camouflage
If Teemo stands still and takes no action for 2 seconds, he becomes stealthed. Taking any action will break his camouflage, granting him 40% attack speed for 3 seconds.

Teemo's passive is perfect at all stages in the game. It is great for setting up traps and fleeing enemies. You can use it in the brush to hide or surprise enemies.

Blinding Dart (Q)
Active: Teemo shoots a dart at an enemy, dealing magic damage and blinding them for a few seconds.
Magic Damage: 80 / 125 / 170 / 215 / 260 (+ 80% AP)
Blind Duration: 1.5 / 1.75 / 2 / 2.25 / 2.5

This skill allows Teemo to harass his opponent(s) in lane. It has a long range and can deal an annoyingly large amount of damage over time. Due to the 2.5 second blind at max level, it can protect you from champions giving you free hits on them, it will work well on anyone who is dependent on auto attacks. This can give you the leg up in a 1v1 fight as you can get many free hits on the enemy.

Move Quick (W)
Passive: Teemo gains increased movement speed. Damage from champions and structures will disable this bonus for 5 seconds.
Passive Movement Speed: 10 / 14 / 18 / 22 / 26%
Active: For 3 seconds, Teemo doubles his passive movement speed bonus. While active, Move Quick's bonus cannot be disabled via champion or structure damage.
Active Movement Speed: 20 / 28 / 36 / 44 / 52%

Move quick is like a free Ghost Summoner Spell but . This allows you to push another lane and get away with ease as the enemy sends half their team to stop your push. Move quick is great for getting in a few more auto attacks or delivering the finishing blow with a Blinding Dart (Q) in lane. Max this second after Toxic Shot (E).

Toxic Shot (E)
Passive: Teemo's auto-attacks deal bonus magic damage and poison his target, causing them to take additional magic damage over 4 seconds. Subsequent attacks only refresh the duration.

Magic Damage on Hit: 10 / 20 / 30 / 40 / 50 (+ 30% AP)
Magic Damage per Second: 6 / 12 / 18 / 24 / 30 (+ 10% AP)
Total Magic Damage Over Time: 24 / 48 / 72 / 96 / 120 (+ 40% AP)
Total Magic Damage for One Hit: 34 / 68 / 102 / 136 / 170 (+ 70% AP)
This is the skill you must absolutely max first (other than your ultimate of course). It has no active ability or mana cost and is applied to all of your auto attacks (passively). This is your primary source of damage and the poisonous effects really add up when you build with attack speed.

Noxious Trap (R)
Active: Teemo places a mushroom trap on the ground, which stealths and arms after 1 second. While armed, the traps grant vision in a 212.5 radius. If an enemy comes within 60 range of the trap, it will detonate, slowing and dealing damage over 4 seconds to nearby enemies within 200 radius. Each mushroom has 100 health and can only be destroyed by auto-attacks.
Noxious Traps have a 10 minute duration. Teemo generates a new trap periodically, affected by cooldown reduction, and can only store up to 3 traps at once.

Magic Damage per Second: 50 / 81.25 / 112.5 (+ 20% AP)
Total Magic Damage: 200 / 325 / 450 (+ 80% AP)
Slow: 30 / 40 / 50%
Charge Receive Time: 35 / 31 / 27

In addition to his other skills, his mushrooms are the cherry on top. They drastically increase how annoying he can be. You can use these to slow down champions trying to escape, lower the health of champions walking through the jungle, kill fleeing low healthed champions, use as wards so that your team are aware of if they are going to gank