I wanted to put this section first so you get get a feel of who, and how I like to play. I'm 'Jakzca' on the NA Server with about 634 wins (1000+ Games), and I've played about 7 ranked games combined (3v3, and 5v5). I would say that I know almost every ability for nearly every champion and know their role (I don't know passives, or all skill names though).

I love playing support champions, nothing satisfies me more than seeing my teammates just get in there and kick some ***, not to say that I don't enjoy that either, I mean.. you don't see Robin just hand Batman his weapons and jumps away, he gets in on that action too. I really enjoy the feeling of knowing that I just made that clutch play, I just saved my allies life and prevented the enemy team from getting that Gold. (Love Janna the most)

Kog'maw fits this role for me, but still branches out and makes me feel like a AP Burst / Ranged Carry. I'll explain more in the next section.

Kog'maw feels to me like a Support, but he also fills that AD Carry or for this build; AP Burster. Playing Kog'maw feels like a guessing game sometimes and he's a bit tricky at first. Try to always be out of the enemies melee range.

Kog'maw's Passive is Icathian Surprise. Upon death, you turn into a Ticking Timebomb, a Total Kamakazi and blow up after 4-5 seconds doing Area of Effect (AoE) damage to nearby enemies. This ability is great if you had a close 1v1 Encounter, or Accidently getting caught early in a teamfight somehow (don't die on purpose :P). I think that even if you cannot get a kill with it, sometimes you can force the enemy to use their flash/ghost.

Kog'maw's Q is Caustic Spittle. This passively increases your attack speed, and on targetting the enemy and using it's (short) range, you deal up to 260 Magic damage and also reduce the targeted enemies Armor and Magic Resist by 25 for around 4 seconds. Most people look down on this ability because of it's melee range, it's true that it has a very small range but if someone happens to get on top of you then just use this plus your Void Ooze (E), or Ultimate (R). Stay calm and make them panic :)

Kog'maw's W is Bio-Arcane Barrage. This ability gives Kog'maw more attack range, and lasts for around 10 seconds when activated, it also does Magic damage based on a Percentage (meaning that it's a great Tank / Super minion killer). This ability is great for giving you some extra range for last hitting, and preventing the enemy from harassing you as much. I think it's more useful Attack Speed / Attack Damage build and not my AP one, still strong though.

Kog'maw's E is Void Ooze. This ability is almost my favorite ability. Kog'maw shoots out Green Ooze dealing up to 260 damage, and slowing the enemy (enemies) for up to 60% for 4 seconds. This ability is an Area of Effect spell (Aoe) and is too awesome at keeping the enemy at bay, preventing them (and punishing them) from/for being too aggressive, preventing ganks, and protecting allies. It's basically an invisible Anivia Wall, they see this and all they want to do is turn away (and should take massive damage if they don't). Even if you cannot accurately hit Void Ooze, just shoot it behind them and delay their escape. Void Ooze is also great for farming and landing this next skill.

Kog'maw's R is Living Artillery. This ability is tied with Void Ooze for being my favorite. Living Artillery basically gives you exactly what it describes, you drop Acid Bombs on your enemy and it's skillshot based. It does Magic, and Physical Damage so no matter what your build, it's still going to be great. It's good to note that it also reveals targets in Bushes, and Invisible Units (Twitch, Akali, etc). In my opinion, Killing with his Living Artillery is probably my most satisfying way to get a kill.

Great Summoner spells for Kog'maw are: Ghost, and Flash to catch up to an enemy, or hop, skip and jump away from one. It's hard for me to place any other skills on Kog'maw but if I had to choose they would probably be Exhaust, or Clarity (specced into it) if you're newer to playing Kog.

Positives
+ Great Range
+ Can be very supportive (unexpected)
+ Two out of his Four abilities are Area of Effect Spells (Don't forget about his passive!)
+ Below the Radar (Not picked as often as say Annie, Malzahar, Gankplank, Twisted Fate)
+ Gets stronger as the game goes on
+ Fun to play
+ Funny Skins (I have the Caterpillar one)

Negatives
- You're so squishy (That Akali and Morde are going to want to eat you instead of you eating them.)
- Besides your Void Ooze, you have no CC and are very dependent on your Summoner Spells.
- Weak early game

I start off with a Meki Pendant because it helps me with my Mana Regen (along with my Yellow Seals) and is a prerequisite for buying your next item, the Tear of the Goddess which is another item that will bring up your Mana Pool, and is a prerequisite for your first item, an Archangel's Staff.

Your Archangel's Staff will greatly increase your Mana Regen, Mana Pool and give you 3% AP based on your Mana. I like this as my first main item because it gives you almost everything you need, Mana and AP to continually cast your Living Artillery, and Void Ooze.

Next up is your boots. I like Sorcerer Shoes for the 2 movement speed (Kog is so slow!) and the 20 magic penetration. These are personal preference and If they have a lot of CC, or/and Magic Users then feel free to grab Mercury Treads, or if you like to Experiment and Theorycraft like I do then grab a pair of Boots of Mobility and give them a whirl. :)

Rabadon's Deathcap is next up because it gives 140 AP, and increases your Ability Power by 30%. After you get this, you should also feel like your damage went up 100% :P

After my Rabadon's Deathcap, I pick up a Rylai's Crystal Scepter because it gives you a bit more HP, AP, and slows whoever you're auto attacking, or using your Q, W, E, R abilities on but, it has a reduced slow when you use AoEs (Rylais probably would be a tid bit overpowered otherwise).

I take a Banshee's Veil, or other defensive item based on the enemy teams line-up and you should do so accordingly. AD? Take a Frozen Heart (Yay, more mana!). Annie, or Sion? Take a Banshee's Veil, this will block a harmful attack (like a stun, that could otherwise kill you) and overall more survivability, since it comes with Health and that's right, more mana! Woo Hoo!

If the game is still going this I'll either try to buy some Elixirs, or another Arch Angels Staff to try to push out even more damage. Remember to Abuse your range.

Kog'maw works really well with quite a few champions, especially melee champions (because Kog is ranged). Void Ooze works great with Xin Zhao, Master Yi, Jax, and Tanky Bruisers like Nasus (who also has a Slow and Area of Effect). Just plop that Ooze down and drop that Living Artillery Bomb, Kablaamo!!

Kog'maw is a utility champion, He's a mixed bag. He's got Attack Damage, Attack Speed (great with on-hit effects like Twisted Fate), and Ability Power. Give Kog'maw a try and I'm sure you'll see that you enjoy playing him as much as I do.

Guide still in progress as I don't know how to add thumbnail pictures, could work on better grammar, pictures, more Synergy tips/allies, and well I believe I can give more. I love Constructive Criticism, and reading your comments. This is also my very first Guide.