Being a strong teemo consists of being able to balance your attack speed and ability power so you can get the most damage per second possible. So combining all the attack speed and the on hit effects give you the most damage you can get. And Remember Teemo Scouts Ahead!

Pros
. Can easily harass his opponent
. His invisibility gives him an advantage in the brush game
. Easily counters almost every top Champ because most are Melee
. Blind highly effective against AD champs
Cons
. Stuns are too effective
. Has only a slow from his ultimate for a 'CC'
. Easy to gank if overextending circumstances
. Not very tanky like most top champs

Starting build:

Boots of Speed, 3x health pots, is the most common way to start the top lane because the boots give you a little escape chance if the enemy Jungler is doing an early Gank. The health pots give you the ability to stay in lane for a longer period of time before going back. Dagger, 2 health pots, is the way i like to start because having the attack speed early in the game gives you more chances to harass your enemies forcing them to go back to base.

Mid-Game Build:
Getting Beserker Greaves gives you the extra attack speed in the early game to give you the time to fire 2 shots instead of 1 to harass your opponent. Malady is a common pick for Teemo mostly because it gives you an on hit effect that goes for a percentage of your AP which you build in the end game items. Zephyr gives you the attack speed you need for that harass and the Tenacity gives you the better chance for escaping if something goes wrong. Wit's End is good for offense and defense it give you high magic resist that will give you a way better chance against AP champs and gives high attack speed. Getting the boots enchant (Furor) gives you the movement if you want to either hit and run or hit and chase it works either way. Liandry's Torment gives you ability power to up your malady and your damage output from toxic shot, blinding dart, and noxious trap. it also gives you an extra DoT (Damage over Time) that gives your more damage if you want to hit and run. The Death Cap is the finishing touch to Teemo's Offensive build it tops off your malady with more damage and your spells.

End Game Build

Liandry's Torment gives you ability power to up your malady and your damage output from toxic shot, blinding dart, and noxious trap. it also gives you an extra DoT (Damage over Time) that gives your more damage if you want to hit and run. The Death Cap is the finishing touch to Teemo's Offensive build it tops off your malady with more damage and your spells.

Defensive (Situational)

Getting Frozen Mallet is an item you want if your having trouble catching a champ that has more speed than you (Very rarely happens) or get it if your fed and want to do a little more AD to end the game. Getting Warmogs is good if you want to have a good AP and AD survival get it if your having troubles against both AD and AP champs harassing you all the time. Getting Guardian's Angel is my favorite pick because of its passive that brings you back to life to kill more champs or to survive. Thornmail is not a very good pick to have for team fights but is good for a 1v1 against that ADC that is getting hand fed to.

Summoner Spells

Flash - Good for getting over walls to escape or to catch an enemy off guard

Ignite - Good for getting an extra DoT on the target and is also very helpful against tanky Champs because it's True Damage

Champion Spells (Abilities)

Blinding Dart - Max this out after Toxic trap. Its used for a blind that will win against AD.

Move Quick - Max last. This is for that extra movement speed you will need to get away or to chase down champs.

Toxic shot - Max first. This is your ability that will give you that DoT on the champ that will take his health down when your not even close to him.

Noxious Trap - Get this whenever you can. This is good for knowing where your enemies are and can also act as a ward. use this in the beginning of the fight to give that really high Damage DoT on the Target.

Masteries 21/9/0

You really just want to get attack speed and ability power so you can do as much damage as possible. you also want that extra armor and magic resist so you can also survive long enough to get all your dots and the target before you die or escape.

Runes

Marks - Get Magic Pen so you can surpass the targets Magic resist to give you full AP Damage output

Seals - Flat Armor Seals give you extra defence against that high Damage ADC

Glyphs - Flat Magic Resist give you extra defence against that high Damage AP Champ

Quints - Flat AP Quints to max out spells and your Malady Passive

This is a Teemo Hit and run build hope you enjoy your next Teemo game using this build. Don't dislike it if you haven't tried it! Anyways my fingers are hurting from typing up this build... Good luck young summoners