This guide will show you how I think you should play Teemo.

I've written about the left Teemo build. The one to the right is simply a fully ap Teemo with alot of Noxcious Trap (Mushroom) damage wich Is quite fun when enemys run In to them and may die (depends on health).

Ignite and Flash Is perfect for this build, you don't need Exhaust or Ghost.

You will have the Rylai's Crystal Scepter that slows with your spells instead of having Exhaust.

The "W" spell wich is "Move quick" already gives you enough speed so you wont need Ghost.

I'm starting off with a Doran's Ring for the health, mana reg and ap.
This will give your blinding dart some nice starting damage for getting the fb.

Next I'm going sorcerer's Shoes for the magick pen and movement speed this will make your damage against enemys higher.

After the boots I save for the Giant's Belt so I'll get more health with the tought of Teemo is quite squishy.

Now It's time for a Rylai's Crystal Scepter with this your spells will slow the target, It's a big advantage If you have to hunt someone down or If you want your Mushrooms to slow them even better.

Now lets do more damage shall we, lets save for the item called Malady It will make you deal more damage in close combat fights with the magic damage each hit.

Wit's End is almost the same as Malady, It's for the extra damage each hit.

Madred's Bloodrazor is also the same as Wit's End and Malady.

And last of all you buy Rabadon's Deathcap to increase your Blinding Dart, Toxic Shot and Noxious Trap (Mushrooms) damage.
Items Summary

Ok now when I've told you some about these items. It's time to imagine what these items will do together at lvl 18.

Sorcerer's Shoes will increase your magic damage on target thanks for the Magic penetration.
Rylai's Crystal Scepter will make you less squishy and will be easier to hunt down targets with the slow.
Malady, Wit's End and Madred's Bloodrazor. These items will together deal extra damage on your target including your Toxic Shot wich will be a awesome burst.
The Rabadon's Deathcap will increase your Toxic shots damage so u'll deal even more damage with it.

For my Masteries I'm using 21/0/9 wich is almost 100% damage including some mana/health reg.
I find offensive as the best spec here because of you'll deal much more damage with Teemo and In my opinion utility aint that good on him.

I've played as Utility Teemo before but one day I decided to try Offense wich I tought was great. You'll deal so much extra damage and still It's a hard time to lose all mana.

For the Runes I'm using Magick pene, Attack speed and Ability power runes.

With the magick pene you will deal more damage on enemys (It reduces their Magick Resistance).
With the Attack speed It's kinda obvious that you will shot faster wich will make you deal damage faster.
With The Ability power u will deal more damage with your spells.