Not Updated For Current Season
Ok, basically what we're going for here is a dps/caster hybrid. Kog'Maw becomes insane towards the end of the game when he can deal ridiculous amounts of damage to a champion using his basic attack.
When building abilities, start with Void Ooze. It makes it easier to farm early on, plus it can be used to escape from faster champions. Ghost and Exhaust also help you escape, but mainly Ghost is there to get you across the map faster. At lvl 6, get Living Artillery - most players doubt the range on this ability, and suffer greatly for it. The first ability you should try to max, though, is Bio-Arcane Barrage. Especially against tanks, this is a fearsome ability. Adding magic damage in addition to your normal attack damage, combined with your high attack speed, and you can decimate any champion in about 10-15 shots. Keep them from escaping with Exhaust and Void Ooze.
Follow the order on the list of items for collecting them. At lvl 18, your attack speed is either at or really close to 2.5, which is the max. By then, you can trade your rageblade for more armor, or more lifesteal. Madred's Bloodrazor or Warmog's Armor are good options to pick.
Early on, Kog'Maw is really squishy, and can't last long alone against enemy champions. Unless the champion can be taken out in a couple of shots and a Void Ooze, don't bother chasing them. Let them come to you, and stay near turrets. After you get the Rageblade, things should be easier. Once you have maxed in Bio-Arcane Barrage, pick one of the champion free lanes and push. Kog'Maw can push through minions easier than any other champion I know.
If one of your inhibitors is destroyed, push that lane. Use Bio-Arcane Barrage on the super minions, since their large health makes them take more damage. You can push lanes with super minions really easily, but you will draw a lot of attention when you start destroying their turrets. Be ready to escape, or if all else fails, be ready to use the one ability I haven't mentioned:
Seriously, a lot of players don't know that Kog'Maw stays alive for a while after he dies, then runs to you and blows up. Most players will actually keep trying to attack you, and will still get caught in the blast. Icathian Surprise does more damage the higher level you are, so try not to just commit suicide with it. You also run faster, so champions that do know what's coming better have a really high move speed, or else they get splattered.
Finally, some tips for using Living Artillery. At lvl 18, the cooldown for this ability is ridiculously low-less than one second per shot. The catch is if you use it within 6 seconds of itself, it costs more mana. Against minions, shoot the back row of casters with the Artillery, followed up by Void Ooze. After 6 seconds, if minions remain, repeat.
Against fleeing Champions, place the marker just ahead of them, and they run right into it. Don't wait 6 seconds on champions - throw as many of these as you can at them until they die. The range is really good, and you can actually go a little outside of the range to fire.
Most of all, stay in a group. Kog'Maw gets ganked easily, so stay near a teammate early on, unless your pushing a solo lane. Go with a tank or high damage champion - Malphite and Cho-Gath are two good partners for Kog'Maw. Use Void Ooze and Exhaust to protect them from enemies, and make sure that you survive yourself. If you do die, just run screaming at them.