Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Kog'maw is a very fun champion once you get to play him, I've played him multiple ways and so far this has been the best.
Now runes are pretty simple for this build. Attack speed: marks, seals, and glyphs. For quints use move speed. Quints are essential to staying alive!! this should give you 28% attackspeed at level 1, which i think is .876 for kog.
standard build down the attack tree with points in the utility tree to finish off. i personally go to the exp but its completely up to you.
These items aren't set in stone but they work best for me. Start the game with level one boots, 2 health pots and a mana pot. Your next item should be to finish your berserker's greaves and then go into a zeal. The extra move speed is needed he's very squishy. Next get the madred's blood-razor, then finish off the phantom dancer. After that i get infinity edge, another phantom dancer (puts you at max attack speed) then i get frozen hammer to finish off.
Max out Bio-arcane the range it gives is your main source of damage, then max out your slime, then your q, getting r whenever possible.
Ignite can be changed to something else but it works for me. Flash Flash Flash Flash, YOU are Kog'maw you neeeeed flash to survive.