Here is my first build, I dont know if it's good, only every time I play with Kog'Maw with this build, I win and got a lot of kills and assists,this build centralizes in attack speed and critical chance.Here im explaining every attack of Kog'Maw and passive skill.And I put the story.
Story: When the prophet Malzahar was reborn in Icathia, he was led there by an ominous voice which thereafter anchored itself to his psyche. From within, this voice bestowed upon him terrible purpose, and though Malzahar was no longer tormented by its call, the voice did not cease its unrelenting summons. This baleful beacon's gentle flicker -- now fastened to Runeterra -- drew forth a putrid beast that ambled across a threshold it did not understand, widening a fissure between the spaces which were never meant to meet. There amongst the haunting ruins of Icathia, Kog'Maw manifested in Valoran with unsettling curiosity. The spark which led him to Runeterra teased him still, urging him gently towards Malzahar. It also encouraged him to familiarize himself with his new environment, to the stark horror of everything he encountered on his journey.

The enchanting colors and aromas of Runeterra intoxicated Kog'Maw, and he explored the fruits of the strange world the only way he knew how: by devouring them. At first he sampled only the wild flora and fauna he happened across. As he traversed the parched Tempest Flats, however, he came upon a tribe of nomads. Seemingly unhampered by conventional rules of physics, Kog'Maw consumed every nomad and any obstacles they put in his way, amounting to many times his own mass and volume. The most composed of his victims may have had time to wonder if this was due to the caustic enzymes which stung the ground as they dripped from his gaping mouth, although such musings were abruptly concluded. When his wake of catastrophe reached the Institute of War, an enthusiastic Malzahar greeted him with an enticing prospect: taste the best Runeterra could offer...on the Fields of Justice.

'If that's just hungry, I don't want to see angry.' --Tryndamere, the Barbarian King
Spells:
Icathian Surprise: When Kog'Maw die, goes into a chain reaction and his movement speed is increased for 4 seconds, when that time pass, Kog'Maw explode dealing damage.
Caustic Spittle: Passive:It increases the attack speed of Kog'Maw, Active: Kog'Maw launches an acid that chase the enemy and inflicts Magic Damage, it's a good combination if you use this skill with Void Ooze, because you will slow the enemy and you can attack him as your choice.
Bio-Arcane Barrage: It increases your range of attack and you deal a percent of the maximum health of your enemy as magic damage. It's useful in ganks
Void Ooze: Kog'Maw launches a Ooze that deals damage and slows enemies, it can be useful in chases.
Living Artillery: Kog'Maw launches a missile from the sky that deals really good damage. It can be useful in chases.
Wish this build helped you.