Basically this is the build i've been using with KogMaw for the last few games. It took a bit to settle on this specific item set, especially since all the guides for him focus either AD or AP. The idea behind the setup is to have huge harassment potential late-game without sacrificing to much of the AD carry build.
These are the standard AD carry runes i use. Armor and MR to counteract the squishy and AD to give early game damage. Other good runes would be MrP or ArP marks and quints depending on your damage dealing focus.
The core masteries are the standard 21 for an AD carry. Your ult scales off AD as well as AP so it's viable even if you plan to stand back most of the time. For the other 9 it just depends on personal preference. Mana allows you to spam your ult more and helps the Manamune's AD boost. I put 3 points into Havoc since it increases overall damage, but you can put these into support to get Runic Affinity (blue buff is amazing on him). The other option is to put them into defense to reduce squishiness.
For items i based it off the standard AD carry build (Phantom Dancer, Infinity Edge, Bloodthirster, Last Whisperer) and then modified it to suit Kog's needs for his ult. I keep the Phantom Dancer for the move/attack speed boost. Instead of Bloodthirster, I build a Bilgewater Cutlass then eventually a Hextech Blade. The spell vamp is great if there's a handy creep wave to Void Ooze. Instead of IE, I build Manamune, and I try to build it early to take advantage of it's passive mana gain. This will eventually give you equivalent AD to an IE while allowing you to spam your ult. Triforce is essential on a hybrid build in my opinion as it boosts all your stats as well as having nice passives. The mana gain also stacks with Manamune. Your last item is situational, but i try to build something with mana. Generally this is going to be a defensive item unless your team has enough CC that you aren't worried about being touched. Options include Banshee's Veil if the other team is AP heavy or a Frozen Heart if they are AD heavy. You can build a Last Whisperer if they're stacking armor.
Pretty basic setup here. I maximize Void Ooze first for it's AoE damage and slow. It helps with creep farming, poking, ganking, escaping, etc. It's your bread and butter ability that is useful in any situation. Bio-Arcane Barrage is your second skill to maximize. It gives you added range and a huge damage increase if they don't have enough MR. I do put one point int Caustic Spittle at level 5 to get a bit of Attack Speed and the Armor reduction, but otherwise save it for last. Living Artillery obviously gets points when it can.
Flash is almost a must since you have no built in escape. Void Ooze in their path then flash away works wonders. Ghost would also be acceptable since you can just run ahead of them while harassing their path to you with Void Ooze and your ult.
I use Ignite for it's extra damage in solidifying a kill. Exhaust works too, but you already have a slow with Void Ooze and anyone that tries to trade hits with Kog 1v1 is an idiot.
The playstyle with this build is super harassment. Once you're level 6 you should be firing off your ult every 6 sec (that's the CD on the mana cost increase). Try to use it when they're attacking, standing still, or dont have any other options on where they're moving to. Use Void Ooze to poke with as well. Try to catch creeps and an enemy champ in the same shot so as not to waste it. Also try to hold enough mana back to be able to use both Void Ooze and Bio-Arcane Barrage during a gank.
Later-game you continue harassment with Living Artillery until the team fight is initiated and then you act like any other AD carry. Don't forget to be auto-attacking and spamming Living Artillery at the same time, though not necessarily on the same target. I often auto-attack the focus while using R on the other team's ranged characters to force them to focus on dodging and less on killing my team.