Hello, my name is Kìngpíns. I am a Silver scrub, however that very fact will not stop me from making a Teemo guide. In general, I am a top lane. I main Gnar, and Teemo. But for Teemo, I have over 134K mastery points (and still counting.) Teemo is one of those champs where you want the enemy to make them hate you as much as you can, but the reason you play him is because you derive pleasure from your enemies's pain. Get ready to evolve into a cancer cell when playing Teemo, because that's what you will turn in to once you start playing him.
(Note: Being a Silver noob that I am, don't expect the wording to be make sense, or be right. This "guide" is really just me expressing my opinion about a new rune build on Teemo. Thank you for being an understanding individual!)

Dark Harvest: DH is the foundation of this guide. With Dark Harvest, you will make enemies cower in fear of the DH Teemo, and also delete them. What DH does: Damaging a champion below 50% of their maximum health by any mean deals 40 − 80 (based on level) (+ 5 per Soul) (+ 25% bonus AD) (+ 15% AP) bonus Attack damage Ability power Adaptive damage and reaps 1 Soul. This cannot happen again for 45 seconds, resetting to 1.5 seconds on champion Damage rating takedown.
This is what will make Teemo OP. You will be able to reap a lot of souls just by procing it with Shrooms, or getting that big damage with your Q. You will also be able to delete enemies with the big burst damage that you will be doing once you have enough items and dmg. Finally, it's a good scaling rune to take.
Cheap Shot: Does bonus true damage when you apply CC. Procs when you hit an enemy with Q or an enemy hits your Shrooms.
Eyeball Collection: Gain extra damage when taking down an enemy or ward, and bonus dmg upon collecting all 20 stacks. More dmg = yes please.
Ravenous Hunter: Gives lifesteal, plus extra lifesteal with enemy takedowns. (Each enemy take down = 1 stack, max 5 stacks, 1 per enemy.) Good for sustain, and staying longer in teamfights.

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Second Rune set: Sorcery.
Celerity: Movement speed bonuses are increased by 8%. Works with your W to go even faster.
Gathering Storm: Allows you to grow even stronger so you can dominate your opponents easily. Good scaling rune as well.

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Bonus Runes:
+9% AS, +10 Adaptive Force, +15-90% HP (lvls 1-18)
You can change the 3rd one to +5 Armor or 6+ MR. Will depend on enemy team.

All you need to do is farm, poke, and get try to proc DH so you can stack souls. And, as an obvious, get kills. As Teemo, that should be easy, as you are a living, breathing, and walking being of pure disease that rots the enemy team of their will, and health.

This stage of the game is where you should be placing your Shrooms around objectives. Also be placing them in and around bushes and be pushing to destroy your turret, even if you're behind. Other than that, farming is top priority for Teemo. You're going to need your items, so farming (especially mid game) is important.

This is the stage of the game where you start to truly blossom. Equipped with items, you seek blood with the amount of souls and AP you have, striking enemies with an auto + Q to put them to rest. That goes for squishy champs, however. For the tankier ones, you just chip them down to death (Tip: Building Guinsoos can really help taking the tankier champs down.) You're still placing down Shrooms near objectives, but also be placing them around lanes you'll be fighting in. In other words, fight with your Shrooms. With you're damage, you should be doing a bunch, mainly with your Q. With turret pushing, you should also be doing a lot of damage at turrets. Pushing turrets, killing your prey, and killing at least one champ is what you are to strive for Late Game.

Hopefully you have put some thought into Dark Harvest Teemo. Let me know any mistakes I made in this whole guide. and I hope you enjoy playing DH Teemo. :)