Not Updated For Current Season
Flash and Ghost are needed, Kog Maw doesn't need any other spells. Kog Maw needs these spells since he's pretty slow and has no escape mechanism.
Pasive: Icathian Surprise
Hopefully it won't come down to you trading a kill by using this passive, but I would not recommend relying on this passive, ever. You want to survive every fight and keep on farming and laning. If you do get ganked, try to explode on minions for extra gold or if you can, kill an enemy champion with it.
Q: Caustic Spittle
I usually don't rely on this skill, it's just an extra attack basically, but it's passive is the main part of this skill you want (extra attack speed). Basically if they're in range for a Caustic Spittle (Melee champs), you might as well use it in conjunction with BAB (Bio Arcane Barrage).
W: Bio Arcane Barrage
This is your winning bread and butter skill. Bio Arcane gives you massive range over your enemies while dealing an additional portion of their hp as magic damage. It's additional damage scales with your AP but I don't really want to build 400 AP just for 4% more Bio Arcane Damage, Madreds is just win all the way. You will use this skill to harass or decimate your opponents (even tanks, but try to target squishies if they are in range). Your MP5 Seals and Utility masteries will give you an enormous amount of mana regen, making you able to harass early game (with good attack speed too).
E: Void Ooze
I mainly put one into this skill in the beginning to easily hit multiple minions and the enemy champ so I may slow him down enough to put around 2-3 Bio Arcane hits into him for harassment (butter them up for a gank). This skill is also very useful for ganks, even if you don't hit the enemy champ, you can still lay a Void Ooze out in front of his escape path to slow him down.
R: Living Artilery
This is another super long ranged attack that you can use in conjunction with your void ooze and bio arcane at the same time (Void Ooze + Bio Arcane + Living Artilery in his escape path). It does have a short delay before landing but very easily mastered to predict where your enemies will run. This skill is also great for map awareness and spotting out champs in bushes. However, if you spam this skill you will find yourself oom so try to stick to the normal cost.
I usually start out with a Doran's Blade or Shield. Shield serves as a more viable way to survive hit-n-run harassments (Kassadin), while Blade helps you with your low AD in the beginning to last hit.
You would usually want to rush your Berserker Greaves because Kog Maw is pretty slow and needs that extra speed to get around. Although you want to rush your greaves, I would not recommend buying boots or a dagger in the beginning because you want to lane as much as possible and farm 24/7.
Afterwards you should go with a Recurve Bow, because by now, your Bio Arcane scales highly with your AS. Recurve Bow also allows you to farm faster and push if your team really wants you to down a tower.
Your Tier 1 item should be Madreds. This item makes your bread and butter skill even deadlier with the additional 4% magic damage. Each hit is going to take off around 10% of their hp. This item is like, BUILT for Kog Maw, the additional AS, armor, and passive makes him so deadly, your DPS will sky rocket after buying this. The additional AD also helps you a bit.
Another great item for Kog. This item gives Kog maw more survivability (HP) and GREAT CC because your range is so absurdly high with BAB you could easily chase down any person. It's like a free Lizard buff all the time. Also take note of your team's CC power, you might want to rush this instead of building more AS.
I get a Banshee's Veil OR a Guardian Angel depending on the enemy team composition. Usually if they are Caster/CC heavy, I take a Banshee's. If they're mixed, I might sub in a GA instead. (BV great for survivability while GA helps massively for team fights, they're both great.)