Read this if you're already in the queue and you need a quick reference

Summoner Spells

CLEANSE and FLASH
This is by far the best combo I've used. Gives you 2 to 3 ways to escape, and when both are on cooldown you're nearly unstoppable.

Items

Buy these items in sequence. Play smart. Harass with a blinding dart followed by an auto attack to apply poison. Stay alive.
Once you hit 6, if you have your philo stone, start being very diligent in placing mushrooms. You'll want to ward your lane entrances, and my favorite trick is putting one just behind the turret as a way to stop and possibly kill turret divers.

Early game you want to have a philosopher's stone built, and be working towards your boots (ideally berserker's greaves), and your malady.
Use your own judgement in item order for the rest. NEVER rush a GA.

Hey kids.

This is my first champion guide, so bare with me.
Please, by all means, offer your advice, but also please please be respectful, and try the build before you bash it in any way. I've tested it over many games in level 30 solo and arranged queue, and it works for me. There's no need to give me a bad rep because it didn't work for you. I'm just showing you how I play teemo.
This is a bare bones guide for more experienced Teemo players. At this point, I haven't added any instructions for general gameplay, so if you've never used Teemo before, try and find a better guide to teach you some playing mechanics. If you can't get the gold, and you can't stay alive, you'll probably fail with this build. This is just my current way of playing, that is incredibly viable, and useful for Teemo.
I'm not saying that this is the best way play Teemo, by any means, but I've had a good deal of success with this build. I almost always have a positive k/d with this build, and you can expect to rack up a large amount of assists, especially if you do a good job of blinding carries and placing shrooms.
There are also a lot of things I don't like about other Teemo builds, so this is my attempt to give my thoughts on playing him.

This match history is from a long long time ago, and the match that is highlighted is using a build that I no longer follow, but the idea stands. I played teemo A LOT back in the day. lol

NOTE: This build was not designed to turn you into an early-game powerhouse that will always grab first blood, however if you're experienced with teemo, it can work wonders for early game. The focus here is to make you a balanced player, get you through the laning phase where you are very vulnerable, and eventually transform you into a mid to end-game powerhouse.

The focus of this build is spread over 3 major things, that I find to be important for a successful Teemo:

1. High regen in the laning and roaming phase.
The starting items may seem wasteful and stupid, but they will ensure that you have some serious lane-staying power, and that you will have more than enough mana to constantly put shrooms down. All the potions may seem like a waste of money, but think of it this way: You can't farm minions if you're constantly out of lane because your health is low. For all intensive purposes, killing 1 minion is basically the cost of a health pot, so it's very worth it in the end if it keeps you in lane. The philo stone will also give you a ridiculous amount of mana regen, and it's an incredibly good item to keep with you until you need the slot empty. If you sell the thing, (which ideally you will if the game lasts long enough) it pays for itself with the gp/5 passive in 6.5 minutes. Seriously. It's worth keeping around for the regen.

2. On-hit effects.
I think teemo is a very unique champ, as the way I like to play him most turns him into a kind of auto attack caster. You auto attack at super fast rates, to apply magic damage. End game when you're attacking, you'll be doing: basic attack damage, poison damage, madred's damage, wits end damage, malady damage, and putting a frozen mallet slow on with EVERY AUTO ATTACK. Twice a second they're going to be taking FIVE separate ticks of damage. It may not seem so strong, but this build will have you doing more damage on-hit with your auto attacks, than playing straight AD would.

3. Survivability
The health from your frozen mallet, as well as the armor from madreds and GA, and MR from the wits end and GA, will beef you up a little beyond the average glass cannon, and provide you with a high probability of survival late game. Between you having all your summoner escapes, move quick, and a slow from frozen mallet, it takes a lot of cc to stop this teemo.

Starting Items

You might be saying to yourself "faerie charm and pots??? Is this guy a ****ing idiot??"
Faerie charm is actually an okay starting item for the gold cost. If you buy that to start, you can afford up to 5 health pots and 3 mana potions, or even a ward if needed. The starting items may seem wasteful and stupid, but they will ensure that you have some serious lane-staying power, and that you will have more than enough mana to constantly put shrooms down. All the potions may seem like a waste of money, but think of it this way: You can't farm minions if you're constantly out of lane because your health is low. For all intensive purposes, killing 1 minion is basically the cost of a health pot, so it's very worth it in the end if it keeps you in lane. The philo stone will also give you a ridiculous amount of mana regen, and it's an incredibly good item to keep with you until you need the slot empty. If you sell the thing, (which ideally you will if the game lasts long enough) it pays for itself with the gp/5 passive in 6.5 minutes. Seriously. It's worth keeping around for the regen. You need it if you're going to roam and place shrooms all the time.

You'll want to get a pair of tier-one boots soon, but it's not a huge deal since putting your first point into move quick is basically like grabbing a pair of boots 1 while youre in lane.
As with any champ there are a lot of ways you can go with boots, but I prefer getting berserker's greaves. They're incredibly good boots for the cost. A thread in the forums did the math, and compared to the cost of other boots, with berserker's greaves you pay the 920 gold for basically move speed 2, and you get the bonus attack speed for 1 gold. These help a TON with early game farming and harass. Late game you can always swap them for Sorc boots if you're in need of some more magic pen.

I don't feel like explaining a lot about the rest of the items.

Basically the whole point of the build is to make you capable of doing crazy damage, while still being able to live awhile in late game. You can use your own judgement to swap out items, for instance getting a banshee's veil instead of a GA. Guardian angel is not one of my favorite items, but it's very well balanced, and if you are very good about staying alive for the most part, this will be a good clutch item for those times when you accidentally get picked off, or you get to instantly come alive after your teams ace each other.

Basically the priority here is:
Noxious Traps > Blinding Dart > Poison > Move Quick

You're basically going to take rank 1 of move quick at level 4, or sooner if you absolutely need the mobility. After that, use your judgement about what to rank up more.
If you're in a lane with 2 ap champs, blinding dart is only really going to be good for the burst damage on the harass. You need to get a feel for your enemies and know your boundaries. If everyone is being very timid and cautious it might be best to rank up poison faster as it will help with your farming, and do more damage overall on the hits you do get off.

You can do whatever you want here, I'm serious. This combo is what works best for me personally. If you're not so great at staying alive, consider picking up health quints or some tankier options.

Magic Pen marks as at least 75% of your damage is magic based. Goes without saying.

The mana regen seals are infinitely useful. You'll never find yourself running out of mana, and that's one of the more important things in the game. Having enough mana is crucial in always making sure you're available to blind that carry and save your teammate, or get out with move quick.

I take cdr per level glyphs, for -8.5% cooldowns at level 18. I know the benefit of per level isn't that much greater, but I take them for 2 reasons:
1. Mid-game to end-game is when the per level start being better than flats. I feel like that's when you'll have the most opportunities to place mushrooms, and make use of the reduced cooldowns.
2. They're also half the cost of flat cdr. lol ;D

Masteries are self-explanatory for the most part. I like taking 21 in offense just to help keep my damage up and it really does help with early game minion farming. You can really do whatever you want, just be smart about it. Just always make sure you pick up Archaic Knowledge for the magic pen, and Awareness for the EXP boost.

Cleanse:
The point of this is to combo it with flash. You're naturally fast as hell, the problem is just when someone manages to land some hard cc on you and you're finding yourself unable to run away. Sometimes merc treads just don't cut it. You're squishy and when you get caught in a bad situation you need to get the **** out NOW. That's why my standard procedure is Cleanse > (am i safely out of range?) If so > move quick. If not > Flash then move quick.

Flash:
The most useful summoner spell in my opinion. It's useful for a huge variety of things, but most importantly ESCAPE. Pairing flash with cleanse is among the most powerful escapes in the game. Cleanse out of cc, run like ****, and flash over a wall. lol

Why not:
Exhaust - A good option, but this build will get you all the benefits of exhaust with your items. Blinding dart, the anti-mage properties of wit's end, and frozen mallet cover about everything exhaust does, except they do it better.

Ignite - Yes, it's kinda nice, and yes it'll get you first blood sometimes, and yeah you can get 10 AP from it with a mastery, but teemo is particularly good at chasing, so I usually pass on this one.

Anything else - Cleanse and Flash paired together are your best option. Whatever else you could want to take just takes away from the power of this combo. You are squishy and people like focusing you. Your goal is to piss them off by never dying, so do it by always getting away, then turning around and killing them later when they're preoccupied.

Well, that's it. I hope this guide has made an impression on you. If people show an interest in it, I'll consider revising it, making it nicer, fixing some spelling and grammar, and adding some more sections, maps, and general advice that I have for playing with Teemo.
GL&HF ;D