Kog'Maw is a ranged champion.
Most players play him with Ability Power build, but I like to make him Attack Damage and Attack Speed.
What's the different?
With my build, Kog'Maw can do high damages with only his physical attack, without using all his skills.

Kog'Maw is very slow; he hasn't much speed. To overcome this problem, I usually use Ghost, which enables him to escape quickly or to easily follow his opponents, and Exhaust which slows enemies and makes Kog'Maw less vulnerable (50% reduced physical and magic damage for the opponents).
If you prefer you can also use Ignite instead of the two spells, just to be sure never to miss the opponent, or Teleport to get there faster in a point on the map.

In the end, my suggestions are:
Ghost, Exhaust, Ignite, Teleport.

The build that I will explain will be slightly modified depending on the opponents you'll find during the game.

The first object to buy is a Vampiric Scepter; we will need it later to complete the Bloodthirster. Vampiric Scepter will charge 12% of your healt, depending on the damage done to a minion or champion.
After, we gonna buy Berserker's Greaves. They give 25% of attack speed.
Third object, the most important one that makes Kog'Maw a strong physical champion, it's the Madred Bloodrazor (+30 Attack Damage +25 Armor +40% Attack Speed. Passive UNIQUE: On hit, deals Magic Damage equal to 4% of the target's maximum Health), starting from Madred's Razor. Then you'll be able to Jungle more easily, making some needful buffs.
Fourth item is Bloodthirster, each killing (minions or/and champions) will increase the physical attack by 1, and life still by 0.25%, for a maximum of +40 Damage and +10% Lifesteal (the bonus is lost after your death, but it is easy to do it again and complete).

After you can choose to buy a Frozen Maller or a Last Whispers: you can buy the second object if you have problems with your enemies because of their defensive builds (such as a tank having armor or many healt). It will allows you to penetrate your opponent's armor by 40%.

Buy an Infinity Edge, which gives you 80 Attack Damage and 20 Critical Strike Chance (unique passive is: Critical hits now deal 250% damage instead of 200%).

If you want to change some items, it will depends on the type of your opponents. More damage or more speed. I recommend a Phantom Dancer.
If in the enemie Team there's a champion who dodges, buy a Sword of the Divine: +55% Attack Speed, UNIQUE Passive: Every fourth attack deals 100 extra Magic Damage. UNIQUE Active: Your attacks cannot be dodged and you gain 30 Armor Penetration for 8 seconds.

I like to play Kog'Maw with Armor Penetration and Attack Speed runes.
At the beginning of the match, they allow me to do more damage to my enemies, and to attack them in a faster way.
If you want, you can change Attack Speed with Critical Chance runes, coordinated with Infinity Edge.
So, I recommend these runes:

9x Greater Mark of Desolation; +1.96 Armor Penetration.
9x Greater Glyph of Alacrity; +0,64% Attack Speed.
9x Greater Seal of Alacrity; +0,76% Attack Speed.
3x Greater Quintessence of Desolation; +3.91 Armor Penetration.

All Kog'Maw's Skills (except passive), are based on Magic Damage. So why do a build that increases physical damage?
If you read carefully the skills, you will be able to understand why (mobafire is backward and has not updated the skills yet, then I will report them to you below).

Caustic Spittle:
Passive: Increase attack speed by 10/15/20/25/30%
Active: Kog'Maw launches a corrosive projectile which deals 60/110/160/210/260 (+0.7) magic damage and reduces the target's armor by 5/10/15/20/25.

Bio-Arcane Barrage:
Kog'Maw's attacks gain 130/160/190/220/250 range and deal an additional 2/3/4/5/6% (+0.01)% of the target's maximum Health as Magic Damage (Max: 100 Damage vs Monsters). Lasts 6 seconds.

Void Ooze
Kog'Maw launches ooze which deals 60/110/160/210/260 (+0.7) magic damage to enemies it passes through.
Additionally, it leaves a trail which slows enemies by 28/36/44/52/60% for 4 seconds.

Living Artillery
Kog'Maw fires artillery from a great distance. After a short delay, the artillery falls dealing 80/120/160 (+0.3) magic damage and reveals targets for 4 seconds (deals 150% bonus damage to Champions).
Each subsequent Living Artillery in the next 6 seconds costs 40/40/40 additional mana

Then here's how the build is linked to the skills of Kog'Maw; if you look carefully the item's Madred Bloodrazor, there's written that its Passive Ability do, to each stroke of the physical attack, magical damage equal to 4% of maximum healt of the opponent. If combined with the second skills of Kog'Maw, Bio-Arcane Barrage, you will do 10% of magical damage (6% + 4%). You have no magic damage, but if this 10% is combined with the physical damage and the speed that the rest of the build gives you, Kog'Maw becomes a good DPS.

Kog'Maw is a real funny champions, but not everyone can play him. If you want to be perfect you need to be aggressive.
If you play alone, try to attack your opponent when you can: stay behind your minion till you have your Ultimate Skill, attacking your opponent sometimes to make him stay away from you and from minion's exp.
If you're playing with somebody else, use your third Skill, Void Ooze, to slow him, then cast your second skill, Bio-Arcane Barrage, to attack him even if you are distant. Don't follow him under enemie turrets, and if you are not with a champion who can stun him. At the beginning of the match, you are not strong enough till you have your final or Madred's Bloodrazor.
When you complete Madred's Bloodrazor, it's time to help allies and doing kills. When you're in front of your opponent use your second skill to attack him, if he's too distant, use your ultimate; if he want to attack you, use Exhaust then attak him.
When you're with all your team, try to attack the one who has more defense or who is more feeded. In that case use your first skill to reduce your opponent armor, then use Bio-Arcane Barrage.

To be stronger, you need to kill minions like Lizard Elder and Baron Nashor (or Ebonmaw if you're playing in Twisted Treeline).

Lizard Elder
The Lizard Elder, when killed, grants a buff where every hit deals bonus damage scaling with level. The buff also slows enemies upon hit. The Lizard Elder spawns with two other Young Lizards. The Lizard Elder's attacks deal DoT, damage over time.

Baron Nashor
Baron Nashor is the most powerful minion. He appears after 15 minutes on the Summoner's Rift Field of Justice.
Killing the Baron gives the "Exalted with Baron Nashor" buff to all living champions on the team that killed him. This buff gives massively increased attack damage and ability power as well as a bonus in health and mana regeneration.
After Baron Nashor is slain, all living players on the team that killed him gain a buff that lasts 8 minutes with the following attributes:

40 Ability Power
40 Damage
3% increase in Health Regeneration
1% increase in Mana Regeneration

Each player on the team is also granted the following:

900 Experience Points
250 Gold

Ebonmaw, the Terror of Zaun
Ebonmaw, the Terror of Zaun is a neutral Minion in League of Legends' Field of Justice Twisted Treeline . Like the Baron Nashor, he is an epic monster.
Once defeated, Ebonmaw will give you and your team a special Buff called Crest of Crushing Wrath that gives the player an additional 1% per Champion-level bonus damage on attacks and spells.

I've always used magic or support champions, it's my first time with a DPS. Anyway, I have no trouble using it, so I decided to make a my own build.
Sorry for my REALLY BAD english, I'm italian D: