I have played 3 types of Teemo's in my entire Teemo lifespan. Firstly, I tried AP Teemo. AP Teemo, to me, was a useless bugger that relied mainly on his mushrooms to rape face. The most notable occasion I had with him was getting a double kill from 2 squishy half-hp heroes that tried to gank me in the bush. I dropped 3 mushrooms there and waited for the party to begin. Asides from that, he is weak in almost everything else.

Next, I went for the more popular AD/AS Teemo build. I thought he was awesome, I thought he was invincible, but then I realized that the damage he actually dealt was not as great as I thought it would be.

Finally, I played a game against this really strange Teemo build that totally pwnt our carries and tanks alike. I was wondering how on earth he could hit so hard and shoot so fast at the same time, when I saw a PD and a Rabaddon's in his inventory slot. Things started to click, and I realized that Teemo relied mainly on on-hit effects to own (toxic shot). So I decided to develop my own AP/AS build. It might be similar to others on this website, but this is my own.

Pros:
Insane damage mid-late game
Crazy mushroom damage despite being a dps build
Make the enemy underestimate you...until you show them what you're worth

Cons:
As usual, you are squishysquishysquisy
The item build is not mana/cooldown centric like the original AP build
If the enemy stacks high MR, you might be foiled

I always go for HP quints for squishy heroes. They need it early game to prevent being raped before they farm up and become formidable. You can always replace them with flat AP quints if you are confident of early game survival.

Marks are AP marks since they are the best at what they do. You are going to need some early AP to have effective toxic shots, plus it boosts your blinding dart.

I recommend MP/5 seals because we aren't going for any mana regen item this build. You'll need it throughout the game, and probably snag some golem buffs to complement your mana regen. This ensures continual mushroom spammage whenever needed. You can also go for per level instead of flats because mana regen is needed all the way (you can get an early doran's ring to compensate for lower early mana regen).

Finally, CDR glyphs are good to reduce the time needed to requisition mushrooms. You will need them if the enemy is jungling all over the place so that you can replaced used ones.

I'm going for 21/0/9, with an emphasis on AP, CDR, attack speed, and mana regen. I'm planning to get an exhaust, hence point taken there. Since we aren't relying on AD, I skipped most damage masteries. Also, Teemo is not a tank, hence 0 for the middle tree. You can place some armour points if you really want to buff his survivability, but it wouldn't help much due to his low base HP.

As your last an final item, if the game still progresses, grab a second deathcap. This will once again catapult your AP, and you should be hitting for an extra 60 damage from toxic shot alone (NOT counting the poison effect).

For your first item, you can choose either Doran's Blade or Doran's Ring. If you need mana regen (spamming blinding darts is your style), then pick ring. If not doran's is a soild choice for early farming and laning.

Next, you have 3 choice of boots. Beserker's Greaves, Sorcerer's Shoes, Boots of Swiftness. Zerker's is my favourite choice as it adds to early AS and every bit of AS is needed for a strong on-hit effect build. Sorcerer's is good too since you are relying on strong magic penetration for most of your on-hit effects. Also, your mushrooms become a tad stronger. I tend to shun this boots though because it doesn't help DPS as much as Zerker's. Swiftness is necessary if the enemy is fast. For one, you do not have a slow, hence it is hard to kill fleeing heroes. Secondly, you might need to run a LOT since you are the main target of most DPS carry heroes. Take a look at the enemy composition then select your boots. If they have MR, get sorcerer's, if they have too many DPS carries, get swiftness, for anything else just stick with Zerker's.

Next you get a Zeke's Harbinger. This will really throw them off, making them think you're another AD/AS build. Unfortunately, all you're doing is stacking some major AS and increasing your survivability (and that of your teammates). Lifesteal is always essential as it can turn a evenly matched fight to your favour. It also prevents you from having to go back to the fountain every time you need hp (the passive regeneration helps with that too). However, your AD is not particularly high, so you might not leech as much life as other lifesteal heroes. Do not rely on it too much.

The major game changer here is your [[Rabadon's Deathcap]. This mother of AP items boosts your AP by an insane amount, helping you snag close to 200 AP with just over 3k gold. With that, the on-hit damage of your toxic shot will rise by about 30 to 40 damage each hit, not counting the sustained poison effect. This makes your toxic shot almost as good as an Infinities Edge, which you aren't getting this build. Furthermore, your mushroom and blinding darts are going to hurt as hell, helping you dominate mid game.

You will need more damage and attack speed, hence the next item: Madred's Bloodrazor. This is the king of all on-hit effect items, and its the secret of how a Teemo can own a tank despite having low AD. It gives you higher flat damage (hence more lifesteal), a bit of armour (more survivability), some much needed attack speed (to bring it close to 1.5-2 attacks per second), and the godly 4% max hp magic damage inflicted per hit. When you max your build (and have about 2.5 attacks per second), you will be able to shave off close to 40$ of the tanks hp in 4 seconds NOT INCLUDING YOUR OTHER DAMAGE SOURCES, which is an insane amount. When it comes to fighting squishies, you can probably down them in 5 seconds flat due to your other damages sources and that plus 48% damage from madred's on-hit effect. You can actually get Madred's Razors as your pre-boots item if you are farming/killing well enough because it's relatively cheap and pays back very well (chance to 1-hit kill creeps). It also helps you to get golem buff, which really helps with early game mana regen.

To boost your attack speed by a considerable amount, you have 2 choices. 1) Sword of the Divine, and 2) Phantom Dancer. The SotD is much cheaper than PD, and it boosts AS by a higher amount (60% as compared to 55%). Also, it adds an extra on-hit effect every 4 hits (100 damage). However, I consider PD a superior item mainly because it increases your chance to crit and it gives you attack speed. While this build is centred on on-hit effects, the chance to crit actually surpasses the 100 damage per 4 hits (you get 1 crit every 3 hits at least, and the crits will deal more than a hundred extra damage). Finally it buffs your movement speed as well. What more can you ask from it?

For your last item, grab a second deathcap. Your toxic shot now deals over a 100 extra damage per hit, and including your poison, close to 90 damage per second. This should complete your AP/AS build.

Alternative items:

Nashor's Tooth
Nashor's Tooth is a really great alternative to SotD or PD because it not only adds AS (50%) and AP (55), but it also gives you 10 mana regen AND 25% CDR. Edit: After some tests, I realized that Nashor's is actually more effective than PD due to CDR, AS, and AP.

Rylai's Crystal Sceptre
This awesome sceptre not only adds HP and AP, but also gives you slow that you've always wanted on NORMAL HITS (due to toxic shot) as well as skills. That's why it's better than frozen mallet for utility purposes.

Hextech Gunblade
I love this item to bits. It gives you AD, AP, and spell vamp + lifesteal. If not for the lack of AS, this item beats stark's hands down. Feel free to swap this with Stark's if you don't mind having lesser AS for more damage per hit.

I follow a standard skill sequence: take mushroom at every level, max blinding first, then toxic, then scamper. Take scamper at level 3 for ganks and escapes.

Blinding actually scales very well with AP. At full build, you can hit up to over 500 damage with blinding alone, making it a viable damage burst. With CDR 30% (from nashor, masteries and runes), you can spam it every 5 seconds, preventing any AD carry from even hitting you. Cast this scale for harassing, and when any hero actually starts to hit you, not before. This maximizes the use of blind. When one hero tries to solo you, shoot him, blind him when he attacks, then continue shooting him. The huge HP disparity after a few seconds should cause him to back off, or put him at a severe disadvantage if he continues the assault. If you invested in nashor's, you can cripple an AD carry's damage by ! 50% ! due to blind's duration (2.5 seconds with 5 seconds cooldown with CDR).

Toxic shot is the main skill this build is based upon. With the full recommended build, you will deal 1.7 x (126+105+0.4x3000) + 90 = 686 damage per second on a 3000 hp hero. This means that he's going down in 5 seconds flat. Factoring in armour and MR, maybe 10 seconds tops. In a teamfight, if you are not being targeted, and the said 3k hp hero is aiming your tank, you can easily take him down in about 5 seconds due to the contributions of your teammates. Following which, you can proceed to kill the other squishies in less than 5 seconds. Assuming you play well and stay at the back (and you have a good tank), you should be able to own most teamfights.

Mushrooms is probably Teemo's most distinctive skill. Say "Teemo" and most people think "Mushrooms <3 !" Good mushroom placement is key to a good game. When you first get mushrooms, place them in the brushes to prevent surprise ganks. This will prevent your enemies from brush hiding, and it may net you a few reversals (they chase you, you enter bush, they get mushroomed, you turn around and shoot them). If your brush mushrooms still survive, (and you are not at mid), mushroom plant the brushes in the river close to your lane. Also mushroom the entrance and exits of the rivers that do not have brushes. This will fortify your position and prevent any possible ganks. Once you enter mid game, ensure that the river brushes are always mushroomed (dragon, baron, and at least 4 bushes near the river). Next priority will be the golems and lizards of both sides. Place them in the brush nearest to the rune mobs so that you can see the heroes (but not the mob). Usually, most heroes won't trigger the mush, so it's a rather long lasting ward that enables ganking. Thirdly, mushroom the forests. Put a bomb on every single brush you see. At late game, put mushrooms at where their base meets the forest. You can teleport to your mushrooms (and so can your allies) to allow for surprise butsecks. Finally, with full build, your mushroom will do over 1k damage each. This means that if you place 3 mushrooms in one brush and wait for a sucker to brush rape you, he will die instead.

Scamper is a simple spell to use really. Need to chase? Scamper. Need to run? Scamper. Need to towerdive (wtf?) scamper. Just don't spam scamper if you need to run back to lane or base, you'll never know when you need it.

I tend to go for exhaust and teleport. Exhaust provides the much needed slow that my original build does not provide (unless you go for rylai's scepter). It can even lead to a first blood if your laning partner is a dps or has another stun (and your enemy didn't get doran's items i.e. he only has 400hp). Exhaust also can be used defensively if you need to run from 1 hero. If there are 2 or more, you are usually screwed.

Teleport let's you get back to laning as fast as possible after an early game fountain visit. Mid game, it let's you defend and farm after pushing lanes. Late game, you can teleport to hidden mushrooms behind the enemies' line of fire to seriously mess with their heads. If your whole team gets teleport (unlikely but possible). You can really screw them up. Or try this. Plant a mushroom behind them (earlier), get one hero to push mid past river, then teleport behind the enemy just as they try to 5v1 him. This will surprise and confuse them, hopefully leading to a team clear. Teleporting to the enemy's jungle can also help deny runes/creeps, and allow for quick pushing.

Alternative spells:
If you're a warmonger, go ahead and grab ignite. Try not to get heal/clarity/revive. They are only good for early game teemo. Rally is alright if you want to push, and clairvoyance is mostly useless due to mushroom wards. Ghost and flash are good escape spells, so you can get them instead exhaust or teleport (it's not necessary to get them both). If you ghost and scamper, you'll probably outrun even yi on highlander. Don't bother with fortify, it just doesn't fit well with teemo (unless you are teemobot).

Teemo is, and always has been, famous for his mushroom juke. Blitz tries to hook you? Plant a mushroom in front of you and blast his face up. Tryn spins you? Mushroom him. Yi alpha's you? Well, you're screwed, cos he won't hit the mushroom. Nonetheless, he might get mushroom juked if he's just alpha-ing to harass. The unstealthed mushroom might waste one of his strikes and since its invulnerable, nothing will happen. He might even get caught when he walks back.

The ultimate mushroom juke is of course the baron mushroom juke. Firstly, ensure that the area around baron is adequately mushroomed (2 mushrooms at baron's entrance, one mushroom at every brush, one mushroom at every escape point.) Next, while they are baronning, go to the nearest brush (they shouldn't be able to see you) and drop 3 mushrooms. There should now be 4 mushrooms in that brush alone (4k damage!). Now, assuming all 5 heroes went to baron, and 2 of them come out with half their hp left. If they all enter that brush, these 2 will die first, and the other 3 will have less than half their hp left. All of them will step on at least one other mushroom, lowering their hp by another 1000 hp or so (depending on MR), and you might snag another 1 or 2 kills. Now scamper around (you're invis in the bush remember? awesome passive) and finish the remaining heroes with a blinding dart and normal hits. There you go, pentakill and no baron buff for them. If your team helps out, more the merrier.

This build capitalizes on insane dps based on on-hit effects and attack speed. It also buffs up all your spell damage, making you a high utility hero as well. Your only weak point is your squishiness, which can be solved by playing well and scampering away when in danger. Good teammates will make or break your game, but you should be able to contribute greatly regardless. This build is in no way a be-all, end-all guide. There are probably higher damaging builds out there that I haven't discovered yet. Play well!