Over the months I've played LoL I've used Mobafire to help me learn how to play new characters. However, I feel I should probably contribute to the site instead of leeching from other people's ideas!
This build is dependent upon having Teemo get as much attack speed and ability power as possible. The changes that were made to Teemo last patch (in my opinion) seem to indicate that he's supposed to be based upon those two things.
My reasoning behind the item sequence and my choices are as follows:
1. Boots of Speed - I feel that these are the best path to take when I play this build (I've tried Doran's Blade as well as Doran's Ring, but I always seem to do better with the increased movement speed)
2. Health Potions - Eh, self explanatory in my opinion (I get two, but you can get up to three or even none at all).
3. Berserker's Greaves - These are simply here because the 25% attack speed increase is nice, the speed 2 is also good.
4. Malady - This item has been changed as of last patch (it now gives 50% increased attack speed, 25 ability power and also deals 20 magic damage upon hit as well as decrease your target's magic resistance by six upon hit, stacking up to four times). This item's ability power boost, attack speed boost and it's effects make it a fantastic starting item for Teemo.
5. Guinsoo's Rageblade - This item is mainly acquired for it's passive effect (but the extra ability power is still nice). The increase in attack speed by 32% and the increase of your ability power by 48 at 8 stacks is very nice.
6. Nashor's Tooth - Again, acquired for ability power and attack speed (the mana per 5 and the reduced cooldowns is just a bonus).
7. Rylai's Staff - This item is very nice because it gives you a little health boost as well as 80 ability power. The main reason I purchase this item is for the reduced movement speed it puts upon your target when you deal magic damage to them.
8. Madred's Bloodrazor - Again, notice the attack speed! Madred's is a great item for any character with a high attack rate, this item is primarily purchased for it's passive.
Whether or not this build is very reliable for anybody else is another story, but it works quite well for me. I've only tested it in 3v3 games and I on average score around 8/2/whatever amount of assists here....