This is my first guide, so I'll start by just posting my build and explaining my reasoning.
Once I learn how to add item shortcuts and get some questions I'll address those.

@Deathalo44: Focused/Altered runes a bit 6/29/11
Added AP Teemo build, just slightly different than the master tactician guides.

Summoners.

Teleport Always, Ignite is your choice.

Teleporting to mushrooms WILL get you kills, my favorite trick is recalling where they can see me and teleporting into the bush behind them when they push. Also handy for countering backdoor pushes.

Ignite I usually choose second because it nets early kills if you come out of your passive and land your burst (poison blind poison poison ignite)

Other summoners

Ghost if you're somewhat new, synergizes well with sprint, allowing marathon speed bursts which can be used in many ways, be it running without a shroom field escape route or chasing someone down for 1 or two extra darts.

Flash Only if you're mid to escape ganks, but honestly, Teemo should never get ganked after level 6 or you did something wrong.

___________________________________________

Runes
Don't pay too much attention to my runes. I can't afford my build yet, and everyone has their preferences. Some people want flat health, which is great for squishy teemo. I mainly just don't like running out of mana, but what ever you do ALWAYS TAKE MPEN MARKS

This is nothing new, poison is key, blinding dart is leveled a little faster than usual because the extra burst often means an extra early kill as the flat damage scales fast and as always...

Mushroom MUSHROOM!

First, why you want to build this way.

You start out with a basic teemo malady/nashors, this is core for teemo AS/CD/AP. It builds quickly and it gives the foundation of this build. The point is to get high attack speed, while lowering/piercing their magic resist in order to make on hit magic damage items and poison release their full potential.

I start out with Boots and 3 pots, because with a little skill you should be able to dodge 90% of all skill shots and harass better as teemo by level 3 (when you pick up the speed skill) giving you more of an advantage than any of the Doran's items IMO since they dont build into anything.

On your first return trip either get two daggers or go straight into malady, this will make you very dangerous as each hit stacks DoT's that get increasingly more powerful.

Next start building nashor's tooth immediately, build stinger (AS/CD) -> Amp tomb -> Nashor's. You'll probably have gotten a kill or two, and minions are cake so this will build fast, allowing you to start mushroom chucking super fast. This gives some nice mid/late laning phase dominance as you can protect yourself totally from ganks.

Choose boots, I take boots of mobility, to ward the map faster, but it's honestly just personal preference. Lucidity for more CD reduc (I max out on blue buff and nashors) merc treads for heavy CC, berzerkers if you need more damage.

From here on out you will start to thrive, if your opponents are tanky dps heavy, start building madreds, if AP or low HP character heavy, take wits end. Both will hit for much closer to their full potential due to malady and you will be spitting darts out like a machine gun, always build the recurve bow first.

Around mid game you'll start to notice your blinding dart/2-3 poison dart burst is losing potential and your mushrooms are becoming less effective. Time for a quick and easy void staff, after you build this I guarantee you'll get a couple of kills because no one expects the huge amount of damage your mushrooms and you will suddenly start dishing out.

Finish with rabadons, mushrooms will be killing for you even if you die, blinding dart will hit like a truck and neutralize AD characters usually for long enough to kill them 1v1 or kite them into mushrooms. Meanwhile your damage will scale perfectly with your enemies, due to resist breaking, percent based damage or the ability to gain huge MR if you're going ap carry assassin.

Frozen Mallet: Great for allowing a few more shots to land, or an escape to be made at your leisure, I usually only choose this if I'm getting focused hard or my team has little CC.
Expensive

Trinity Force: Solid item choice, gives you a little bit of everything AND more movement speed which is nice, a good choice (along with lich bane) if you want to rely more on auto attacking.

Lichbane: Since you usually are forced to choose between this and rabadon's or void staff, I like to leave this aside, but I can see the merit in the BD->Poison nuke on VERY ap heavy teams, a good choice with wits end, replace void staff

Shoes: Just don't choose boots of swiftness, all the boot effects are great on teemo and it will be up to your judgement which is needed that round. Just a quick note, if you don't think you can get blue buff often, take boots of lucidity to get near the CD cap.

Also, an aside, if you have a stealther on your team they are going to get oracles. They will kill your shrooms, your AP usefulness will be halved, Start building to capitalize your auto attack damage.

Why I don't go straight hybrid

There are two specific items, which initially look great on Teemo, but in reality just don't quite fit.

Guinsoo's Rageblade: You have incredibly high attack speed, and this helps build everything you want right? more AS, ad, huge AP and all for cheap right? Wrong, stacking AP doesn't benefit your mushrooms when you're not stacked, and the only reason you build AP is for BD and shrooms (and since you use BD within the first couple shots it usually isn't stack backed either). Great if you went pure hybrid for early lane harass, but useless here. If you want to get it, only get it if you're fed early, otherwise there's better options.

Hextech Revolver: You are squishy, very squishy, if someone wants you dead and you can't run, you die. Spell vamp/life steal aren't gonna change that much unless you are capping an AD/DPS build (with blood thirster as well) or if you have the frozen mallet to boost your HP. Your job as teemo though is never to get hit, and never to get ganked. You have the tools and the speed, so I find this over priced.

Newly added. Mainly for use when you think both teams are weak (IE, no tanks, since this is a better option for a backline teemo). AP teemo can net your team plenty of kills, protect retreats and carry, but should not be in the middle of team fights. KNOW YOUR ENEMY, know where team fights break out, shroom around them, and once they break out your presence is already made, cut off retreats and blinding dart any ad carries or anyone under half health. Toe bombing is also quite viable, but be cautious.

The point of nashors tooth is just because it's a strong slow build item for teemo, gives you what you need cdr/AS/AP, and keeps your opponents guessing early on so they won't start planning immediately for oracles/MR.

Once you're half done with the stinger get your mejais, stacks will come, teemo's awesome at getting away. Basically the only difference here is we're sacrificing dps for burst damage and shroom kills (which are hilarious).

I take duo lane or mid, never take a 1v2 lane if you can help it though, because you need to be able to harass and plant your key shrooms, having two targets makes it much harder to dodge skill shots, and you go down fast if you're stunned.

If on top or bottom, race two near center of the lane and go invis, you should beat your opponent, try to position yourself so your vision only just allows you to see if someone enters your teams side of the bush. Wait for the champs to show before revealing yourself, if they're squishy, poison the hell out of them with the passive AS boost, if they're tanky, just take some pot shots hit a minion and run and lane like norm.

Your burst Teemo can take almost any carry down IF he can land his magical burst combo early game, from invis (and you can just invis in a bush and rush out) poison, blind, poison poison ignite. You will get the kill if they allow you to hit them one more time as they're running, otherwise you just forced them out of lane. Do not attempt against a stunner with their stun off CD

Mushroom Placement

Cover your lanes ganking sites first (all bushes) followed by the antibush side walls (or if mid, the 4 corners.) People avoiding your bush shrooms or trying to chase you will often run into the opposite side wall shrooms, temporarily forgetting you don't have to place them in bushes.

Mid game, cover up mid lane bushes to protect your carry, then cover all of mid to make life hell on the enemy team attempting to be sneaky with their ganks or counterjungle. If you've covered that, start placing them in highly traficked intersections in the jungles on BOTH sides, this gives escape routs to your team and gives you the true edge in map control.

Late game push: Put a mushroom on every entrance to the mid lane as far as your team has pushed, this allows your team to be less wary of ganks, and more willing to attack knowing they have multiple paths of escape.

Mushroom Tricks

*The Incredible Mushroom Con Gank* Recall under your turret if they've pushed you back and you're at low health. They see you do this in solo queue and they WILL try and damage your turret if they haven't recalled themselves. Teleport to the riverside bush shroom seconds later at full health, lay your burst down and poison them the whole way home, as they have to run past you to get to run away, or run into your shroom escape route if they think they can give chase.

*Mushroom bush gank* About the same as above, but choose a target if your team is heavy with teleporters, get everyone to teleport to the same bush and voila, instant total surprise gank or backdoor.

*Shroom kiting* Set up a predestined path with shrooms on both the path and the exits from the path. Find an AD Carry/Tanky DPS and they will chase you, because you're teemo. When they've finally decided they're done wading through shrooms they turn, running in to one of your exit path shrooms and you kill them while they're slow and weak and blind.

*Toe bombing*
In most situations a mushroom laid in plain sight will just get avoided or destroyed. There are two times this will turn the tides though.

The Team Fight: In the middle of a team fight, people will be taking down champions, this means you can set your mushrooms at dead center and nail their whole team, or set a deadly escape route (behind your team) or choke (circle behind theirs) in plain sight, they will ignore you 90% of the time, and forget the shroom placement in haste to chase/run almost as often.

The Kamikaze Sometimes you get slowed or stunned, running is not an option, a blind won't last long enough, and you have no near by escape route or comrade.

Turn and face your opponent, blind them, poison them, throw a mushroom under their feet, ignite them, poison them, die, get the kill from the insane DoT they allowed you to get since they were so busy rejoicing in the fact they killed you, the most annoying character in LoL.

Lastly

The Blind Feint
AD Are strong, but dumb. Once your blind is maxed it will last for almost 3 seconds. Blind them, toe bomb them, run while they're slow, then finish them off or run away while they attempt to close the gap. When they are blind, an auto attack based champ is reduced to nothing, don't be afraid.

So give it a shot, I've had a ton of success, if you get some nice scores post em up, and if you know how to make item links I'd love to know how.

I'll post my scores up as soon as I collect them.