Not Updated For Current Season
I go for ghost and heal. ghost is very important for kogmaw since he has little ways to run from an ambush , or you can use ghost on a fleeing champ to quick getting the job done. Heal can help you hold your lane more and thus getting more levels and money quite early . it's also important if you are alone on the lane (whether it's a leaver or your teammate died) the other team will start craving for you especially if you have low hp , keep your heal until they come under turrent and surprise them with it when they are very close.
Mastries and runes
I go for armor penetration . why ? as you can see , Kog's first ability penetrates the armor , imagine if you already had 29 at the beginning ( + 6 from the sunder ) that's 35 plus your first skill which will make you deadly. you will also need the magic penetration of the offence. you might not need the critical though BUT my build is based on long going games , so you might want to grab Phantom Dancer instead of the Hextech Gunblade.
for some of you , my build might seem kinda weird or stupid so let me explain. start with Doran's Blade for more hp which will help you hold your lane and get some money before heading back shopping.
for the second item you will get Berserker's Greaves for increased movement and attack speed.
next is the legendary new cheap item. why would kogmaw need manamune ? kogmaw thirsts for mana , at level 18 your mana will be 2000 + . also , you will get crazy damage by the same time equals 220 + . thus you won't need to spend huge gold on any other damage item.
your third item would be Last Whisper. you will start raping the other team with this item since you already have crazy armor penetration , and you'll get extra attack speed.
next is survivability that's why you need to get Frozen mallet . you can either have phage and go for another health item . or you can just get the 1975 gold to complete your phage.
as for the hextech gunblade , it's not quite neccesary unless the game goes long , but it will give you some awesome AP and Damage.
my last item of choice would be Banshee's Veil , it's really helpful in team fights and the cooldown is only 30 second , plus you'll get extra hp for more survivability.
I don't about gameplay though I have 2 things to note. the first is kogmaw ulti , when you have enough mana , keep harrasing the opposite team quite quickly with it , you might get a kill , or you can get them to a critical state , both are helpful. second is that whenever you run from someone , remember to cast your void ooze (w) toward them to slow them down. the rest is up to you .