This build is partially the way I use to play Teemo. As it is, I'm a fairly new player to LoL, and so the rune build is something I would like to have eventually, but rash purchases in the past have left me with not as desirable runes. Nevertheless, my Teemo can make a significant impact on the battlefield. I play Summoner Rift mainly, and almost never Twisted Treeline, or dominion. If you find this build successful in those arenas, it'll be great, but since I almost never tried it there, I can't promise you it works.
Of course, eventually the success or failure depends mainly on the play style of you and your fellow summoners, the tactics you choose, and how well you execute them. I found this build very successful in most variations of teams, since Teemo is so simple to play, and yet always helpful to the team.
My play style is no good for middle lane. I honestly don't know how Teemo can keep up in the middle lane against assassins. But when it comes to solo top, or bottom lane (with support/off tank/tank) this build works wonders.

The item purchases for Teemo as an AP hybrid are pretty comfortable. You'll almost never find yourself recalling back to heal, without enough money to buy something... The first items I am suggesting for Teemo are all relatively cheap, and are all built from cheap ingredients.
The item sequence is, of course, not a rigid one. If you feel like you want to start with Malady before Phage and Fiendish Codex, it can also work, depending on your play style. Or you can choose to have Trinity Force instead of Frozen Mallet, Will of the Ancients instead of Hextech.
I used to start with Malady, putting the emphasis on Teemo's poison, but I later realized that Malady gives little to no bonus, when your poison is still weak. And so it is more important to have a little more AP, and more cooldown. The cooldown is very helpful for Teemo's ultimate. Don't go over your head with cooldown in the beginning, as you wont have enough mana to use your skills that frequently anyway. It will be much more of a help to have a little more health buff, slowing chance, and magic resist reduction, before you move on to completing Nashor's Tooth.
So my suggestion stands, as it shows above.

Teemo's ultimate is a unique one. It will not change the balance of a team fight, like Karthus', Ezreal's or Lux's ultimates, nor will it take out a single enemy (unless lucky), but it will give your team an important edge throughout the match.
Placing Teemo's shrooms in key locations around the map will give your team a huge advantage. Aside for being great damage dealers and a general pain in the enemy's butt, Teemo's shrooms work as wards for 10 whole minutes (or until stepped on). This gives your team a wonderful map control and saves a few coins. So place your shrooms in key shrubs and near the Baron and the Dragon. With enough experience you will notice bottleneck locations, where the enemy frequently crosses. Placing your shrooms there will help you chase them down or escape them in the future. In that sense, Teemo is a support champion.
At level 16, with all the cooldown items complete, you will have another shroom ready about every 17 seconds. Don't save them all for warding, as the do make an impact in various situations. When a team fight is boiling up, make sure you plant those shrooms around the future battle zone, to give your team a great advantage. Place one or two shrooms behind your team, in case the fight will not be successful, to give the survivors a better chance to escape and avoid being aced.
Teemo's shrooms are also very useful when farming giant groups of creeps later in the game. One shroom takes down 80%-90% of those creeps and you can quickly pick up the rest, ending the whole thing in 2 seconds.
When team fights erupt, my sneaky Teemo has two tricks up his sleeve. Use blind on the AD carry, and exhaust on the AP carry. If you had your exhaust ready, and you managed to cast both right away, you have given your team a huge advantage! You basically neutralized the two greatest threats for a few seconds, giving your team enough time to kill one of them - both, if they are coordinated and experienced enough. Immediately after casting those two spells move on to auto-attacking prime targets. If the fight was successful and now the tank and off-tank are running away, it's time to "move quick" and with the help of your Phage/Trinity/Mallet you will hunt down any target.
The slow effect of Phage/Trinity/Mallet is also quite useful when in lane trying to chase down your wounded foe. Teemo's poison usually makes over committed attackers to back off in horror. Having slow effect will help you chase them down and add a little more potency to the poison, bringing them down, if they weren't close enough to their turret.

The Pros for my Teemo build were posted above, as you should always base your play style to your strengths. So this thread will focus on my Teemo's cons.
Every hero has his disadvantages, to make the game a fun and interesting one. It is important to always remember those cons to avoid unfortunate results.
Teemo's one great disadvantage is his vulnerability. Riot has recently released an interesting list of statistics about the game, where it stated that Teemo dies 75 times per second world-wide. Teemo is an easy target to kill, and in team fights he will be one of the first to be targeted, unless you keep your distance. Don't be too risky when placing your shrooms before the team fight, if you wonder off just a little in front of your group, you will invite the enemy to jump on you, kill you, and have a 5v4 team fight.
My build offers little to no defense and resistance. So keep that in mind, until you have your Guardian Angel. Teemo is a ranged champion, but his range is not too great - any champion with a bursting force (ww, voli, xin, ezreal, fizz, kassadin, and many others) can easily grab you and make you regret you initiated a fight with them. So stay behind your creeps, and keep an eye on enemy movement, be sure to run back, just a little, at the slightest hint. Teemo has a constant movement bonus - it will keep you alive if you are paying attention.

Thank you for reading my guide. I hope you won't use my Teemo against me.

Any notes will be gladly taken, as we can always learn more, even about our favorite champions. I am still losing with my Teemo from time to time (*the noob teammates are to blame, of course!). So try my build out, give me your feedback and always remember to blame you noob jungler, if something goes wrong. No, but really, take responsibility to your poor actions, if and when the occur.


*that was a joke...