Have you ever faced a Kog'Maw that you feel you can go 1 on 1 against and make it out alive, and one of two things happen?
1. He kills you. Flat out embarrasses you in front of your entire team, while walking off with half of his health left.
2. You manage to kill him and have a tiny bit of health left, but he suddenly runs up to you and finishes you off?
Well, you can be this annoying Kog'Maw, stacking up kills and dealing tons of hurt to even the best-built tanks. This build focuses on building pure attack damage and speed, which will allow you to elegantly finish enemies with 3 simple clicks.
*THANKS TO ZOKROTH FOR EDITS*

Since you've picked to play a carry, you want to really do the carry's job. A carry, after good building, will be able to kill someone by right clicking them (and maybe a few abilities to make sure your target is gone for good) Armor penetration is emphasized with quintessences and marks to build it, and your speed will be added with seals and glyphs.

In offense, you only want to get your exhaust boost and magic penetration, which will let your Wit's End and Bloodrazor hit harder, and your abilities even more painful. The 21 in utility will give you the edge on a lot of aspects, including movespeed. If you end up dead and want to finish off the person who killed you, but didn't run away in time, you'll be able to catch up to him. Extended experience so those nooblords who feed you will be underlevelled even faster.

If you just saw the length of this paragraph and feel like tl;dr, then heres the point:
Follow the order of item buying, right click to hurt lots.

I always say building is everything, and when you're a carry, you're going to need to build quickly to make sure you don't find yourself outmatched going head to head with an enemy champion. Start off with a Doran's Blade, because the 100 health it gives you and small damage boost will find itself useful early. Get your Malady for a 50% speed boost and a little AP. Its passive that will haunt enemies trying to escape, when you suddenly use your Void Ooze to slow them, because you'll find its damage satisfactory. Wit's End's on-hit damage will be of use since you haven't been able to afford a B.F. Sword yet, and the added magic resist will make 1v1 fights against magic users much easier. Get your Bloodrazor components as you go, so when it's finished you'll be able to anti-tank effectively. To add to that, a Black Cleaver can remove 45 armor in 3 attacks, making it easier for you and your team to finish someone. Get your Bloodthirster so you can finish fights without having to recall constantly. Finally get the Last Whisper to add the last bit of damage you'll need and even more armor penetration. (Sorry if this explanation is a little wordy)

Get your W (Barrage) early, because you want to outrange people to hurt them. This prevents early damage which will reduce the risk of feeding an experienced enemy. After, catch up on your Q (Caustic Spittle) so you can passively increase your attack speed, and have another huge-damage factor on your side. Open up with Q, rapidly hit someone, and they won't have a chance to fight back before they decide to run or flash the heck away. Get your E (void ooze) more often later, because it wont find itself as useful early as it will in teamfights, and its mana cost is a little heavy for early game Kog'Maw. Use your R as spaced out as you can to prevent using 200 mana for what could cost you 40 to harass those dang turret huggers even further, or to check that bush the enemy keeps hiding in. Eventually, your going to find yourself 1v1 against someone (let's say, level 13) If they can see you, slow them with your E, hit first with Q to remove their armor and magic resist, then right click and use your living artillery to hurt them. If they try to outrun you or flash, you can hit your W to add some range and finsh them, or place an artillery shot right in their path, so they can find themselves slapping their foreheads for walking straight into their death.

So, for anyone who thinks I talk too much, here is as bare-bones as I can get:
Build high attack speed, damage, and on-hit magic damage items to hurt your enemies. Use Q to make their armor and magic resist lower. Use W to outrange someone who's sitting way in back of a team fight or any other situation where you need range. Use E to deal pretty nice damage and to make enemies' escape attempts futile. Use R to finish, harass, find hiding enemies, etc.

If that's *still* too long, here's the jist:
Don't die, hurt lots, victory dance.

But the build isn't enough. Only with practice will you become a master.

Also, don't waste mana farming. Just shoot as fast as you can, and it'll get the job done. I don't think I'll see a well played jungle Kog, but if I do, I'll let you know.