Hello! This is my first ever mobafire guide and I hope you find it useful. Any comments as to how I may improve this guide would be great!

In short, the way I play Kog'maw is as a long range sniper. I will go through the key points in playing him in this fashion, explain why I chose what I did, and give a few tips to make this a lot easier.

Pros:
great farmer
-farming is moderately annoying early-game, but just about as annoying as it is with other champs.
long range
-possibly the longest non-global ult in the game.
consistent damage
-no pesky CD's to worry about! only constricted by mana, as his ult doesn't have a long enough CD to worry about.

Cons:
super squishy
-if an AD carry gets into range of kog, without any assistance, kog will more than likely die.
requires lots of practice

Ignite
Personally, my favorite. It really helps you get early-game kills when your sniping range isn't quite what it is late-game. The only downfall to this is that it has no defensive use. Use this if you feel very confident in your positioning, and don't need Ghost to help get away/chase. I personally use ignite for a better early-game.

Flash
An absolute must on Kog'maw. While he may have a slow, he has no other forms of getting away from his targets. If they are on him with gap closers ( Spinning Slash, Riftwalk, Bladesurge), then flash will help mitigate damage and allow you to dish out more from a safer distance. Quick tip, use your Q before you flash out (if you can).

Ghost
This is another spell that helps with positioning. I don't personally find it useful, but I have ran into points in a game where I think "If I had Ghost, this guy would be dead." Ghost is a lot better end-game in comparison to Ignite because it allows you to stay within range of your target longer. Ignite could possibly finish them off, but having ghost to catch them with your R is a lot more dependable than hoping your ignite (which is a fairly close range) finishes them off.

Clarity
If you need this, you're spamming your skills too often.

Teleport
Semi-useful. If you find yourself having to get around a lot more (can't stay in lane), then this might be more beneficial than the others.

Anything else is pretty much a no go.

Greater Mark of Magic Penetration
Most AP champions need Magic Resist Penetration, and Kog'maw is no exception.

Greater Seal of Scaling Mana Regeneration
Kog has mana issues pre- Tear of the Goddess, and a little bit into it. Nothing a blue buff won't solve. Having mp5/lvl seals will help early-game with harassing.

Greater Glyph of Scaling Mana Regeneration
Same as seals.

Greater Quintessence of Ability Power
Kog needs a little bit of AP early-game to make your enemy really feel the pain. These help with that, so that you can buy boots first.

You may swap these out the mp5/lvl for AP or AP/lvl runes. The AP runes would be more useful if you are extremely confident in your ability to land skill shots/harass your enemy.

9/0/21 is pretty standard for an AP.

9 points in offensive because:
Extra MrPen. That's it really.

21 points in Utility because:
Move speed is needed. Positioning is important on Kog.
5% Max mana helps stack with your Archangel's
I get 2/2 in Utility Mastery because I love blue buff. As AP Kog, it is a godsend.
I only do 1/3 Good Hands because as this kind of Kog, I really don't die that much. Even when I do, the extra seconds for me to come back alone aren't usually that helpful.

Early-game (1-5)
No matter what lane you pick (I love mid as Kog), just farm last-hits. If you have mp5 runes, harass your enemy while landing last-hits with your E. If you went with AP runes, use your harass only to hit the enemy. If you can get last-hits, great, but don't go too out of your way. Farming is important.

Mid-game (6-13 or so)
Keep farming. Now you have become the ultimate harasser with your R. There are only a few champions that you can't just zone completely by existing (ones that can pretty much kill you in a quick second Akali). This is where your "skill" really shines or falls flat. When harassing with R, try and let the stacking debuff fall off in between hits (so that it doesn't cost too much mana), unless you are going for a kill.

Late-game
This is where team fights usually start happening. Depending on your team comp, it may be better to stay close to your team, or way in the back (but probably in the way back, as you are a prime target). In team fights, use your E to hit as many champs as possible, and spam your R on as many targets as possible. Personally, don't "focus" the "focus target" because he is usually in the midst of everything, and you can hit him and multiple others. You'll find that multi-target snares are your best friend for team fights ( Amumu, Galio).

Farming early-game gets to be annoying. Just last hit with normal attacks. If you are in a side lane and can't even get in range of your basic attack, last-hit with E, or turn on your W to last-hit. Once you have a decent mana pool, you can R right after your E to kill off caster minions, and then farm the soldier minions normally.

If you get really fed/farmed, your E should just kill everything it rolls into. Many times do I see just a river of gold numbers =).

I start with boots because Kog without boots is too vulnerable. It also lets you go in/out for last-hits a lot easier.

Next I rush a Tear of the Goddess to start building up the mana benefit. Once you get this, you shouldn't run into mana problems. When simply harassing, use your R only once or twice, any more than that is not worth the mana cost.

Here, I (personally) rush a Mejai's Soulstealer. This, for me, is usually around 11 where he can really start pulling the kills in. When played correctly, Kog almost never dies since he is always in the back, so you usually keep your stacks.

After Mejai's (or even if you skip it), I usually upgrade my boots to Sorcerer's Shoes.

The next items depend on how well you are doing. If you find yourself dying (or you skipped over the Mejai's), get a Rylai's. This really helps you finish off those pesky runners with your R. The bonus health is nice too, for surviving what burst damage may be coming your way.

If you are dominating your lane, you can skip right to a Rabadon's Deathcap. This will boost your AP and if you get a Mejai's, can put your around 300 or 400 AP as only your second AP item.

If you did NOT get a Mejai's, I recommend getting an Archangel's Staff AND Rylai's Crystal Scepter before your deathcap.

If your game lasts long enough for you to finish Archangel's, Rylai's, AND Deathcap, then you have a few choices. If you didn't get a Mejai's, then you have even more choices. And here are some options available:

Void Staff
This is good if the opposing team is stacking magic resistance. If you did not get a Mejai's, definitely consider one of these.

Lich Bane
I love this item. The move speed is great, and the passive gives Kog a lot of burst (his Q, E, R, and the passive). The best part is that it synergizes well with his W. You can do a lot of burst even at a distance (with just his R and W).

Deathfire Grasp
This item is good only if you find yourself in a 1 vs 1 scenario, or they are bursting you down really fast. However, if they are, you should consider your positioning. When playing this style on Kog, the opposing team should have to go through your WHOLE team in order to get to you. If you have this AND lich bane, some crazy stupid burst is possible (lich bane passive, this active, Q, E, R).

Needlessly Large Rod
If you just need to fill in one spot before the game is finished, this is the best AP per gold item out there. Otherwise, there are better things.

Will of the Ancients
I used to get a Hextech Revolver early-game to stay in lane longer, and turn it into this... but I just don't like it any more. The AP is okay, I suppose. Consider getting other items.

Zhonya's Hourglass
Do not get this item. An extra 2 seconds to stay alive is more than likely not going to help you if they are already in your face. If you just want a lot more AP, get another Archangel's.

Here are some miscellaneous tips:

When a melee gets into your face, there is little to no chance of escape. Try killing them instead of running! All of Kog's abilites can be used at once and can surprise your enemy, and maybe even cause them to run away!

ALWAYS check bushes with your R. Never face-check.

Like all skillshots, try and anticipate where your target is moving when using your R. However, unlike (most) other skillshots, Kog's is spammable. I find that most players try and avoid his ult in the same fashion (running in the same direction, usually). You can put this directly over the target to see how they dodge it. If they move to the left, next time, place it slightly to the left, they might run INTO it instead.

Also considering his R, some people are just really good at avoiding it. Sometimes it might be best to just put it in their general direction. Alike the prior tip, people can start anticipating how you shoot your skillshots. Don't be predictable.

Don't ALWAYS use your R. A lot of people also get attuned to the range on it. If you get within range and not use it, it may give them a false sense of security. You can then hit them with many in succession as opposed to just one.

ALWAYS lead fights with your E. Positioning your E is very key. Try and make it so that the enemy has to run over it to get to you, but also hitting targets. If running away down a straight line, consider putting your E in front of you instead of behind. This way, they will have to run over the full length of the slow instead of just a sliver of it.

If you are oom, or close to oom (for some reason) don't forget Kog's W! It scales with AP as well. End-game, I've had it shred players for 14% of their max health (base 6% + 1% per 100 AP). I've finished games with 800 AP before, and sometimes, W is better than spamming R (especially if they are a heavy on health Cho'Gath).

Positioning is key! I cannot emphasize this enough. Kog is super squishy. Building defensively will, more than likely, fail you. Flash is pretty much your only dependable escape. He has such a long-range and an ultimate that reveals underneath. There is no reason somebody should be sneaking up on you (with the exception of stealthers Evelynn, Twitch, and even good Shaco's).

Use walls to your advantage (this goes with positioning). Kog's long-range can mean that there's the possibility the other team won't even know where you are during the team fight! Many team fights in the jungle are this way. I have been in a team fight in the river between dragon and middle lane, and I stood at the bush to the upper-right of Blue Team's red buff. They never touched me. Nobody even came close.

Get blue buff, this helps Kog so much! If you are greedy (like me... a lot of the time), I intentionally try and get the killing blow on enemy champs with blue buff. Plus, it's fun if you're playing with friends =).

Even while running away, you can kill people! Because you should already be in the way back, the enemy should be chasing your teammates instead of you. Don't leave them for dead (unless they have someone who can close gaps really fast =X)! A lot of the times, I've found ourselves losing a team fight, and then they chase for the remaining kills. If you use your R to hit them while they are chasing, they can get low enough where they have to back off or die!

Also while running, save your E for a good time. A lot of the time I just use my R to help while they give chase, and turn those into kills (and using E afterward!). Using E will usually just help them get away, and probably will not yield any kills. However, use your judgement. If it's a 2v5, then just get away. However, if it's a 4v5, and your team is just low on health, consider just using R to turn the tides.

Stack your Tear of the Goddess ASAP. If you go back because you're low on health, but not oom, spam your abilities to stack it up! However, don't spam so much so that your mana isn't full by the time your health is. Even when I go back because I'm oom, I still usually use at least 2 abilities (W and R, since they are the cheapest in mana). Also do this when you have blue buff.

Anyway, that's it for this guide! As I mentioned before, let me know if you have an questions, or think there should be further explanation, or even if it sucks! But please, be constructive =).