Well for starters, it's not really an AP build. Kog'Maw has pretty mediocre AP ratios, so stacking high AP isn't too effective on him.

This build focuses on MRPen (higher damage), CDR (more constant damage) and MP/5 (to keep doing damage). Naturally, the items with these three stats also come with AP, and usually you'll get enough AP out of them to boost your skills' base damage up.

To play APC Kog'Maw effectively, you need a lot of practice with skillshots. A LOT. His ultimate has a 0.6 second delay, which is pretty easy to dodge for an attentive opponent. Usually rylais is one of his core items, because it makes landing consecutive shots a lot easier, and also allows you to permaslow an enemy across the map (the Rylais slow lasts 1.5 seconds, your ultimate has a 0.6 second delay and can have a 0.6 second cooldown with max CDR) which can be incredibly useful for chasing down a fleeing enemy.

Kog'Maw's AP ratios are pretty terrible for an APC at first glance, but you have to keep the following in mind:

• Living Artillery damage is multiplied by 2.25 against champions, meaning the base damage at level 3 is 360 (+ 67.5% of your AP). When you have some magic penetration and Liandry's Torment, this puts your long range damage pretty high. With max CDR it has a 0.6 second cooldown, if you have 500AP it'll deal 360 (+338) damage every 0.6 seconds. That's a whopping average of 838 damage per second, assuming you land every hit.
• Your Caustic Spittle reduces enemy MR and armour by up to 25, this on top of the 15 from Sorcerer's Shoes, the 15 from Liandry's Torment and the 29 from your runes, totals -84 magic resistance on your target. Against squishies who don't have more than one MR item, this will most likely put them into negative magic resist, giving you bonus damage.
• Your Bio-Arcane Barrage scales with AP, late game you should be doing 10%-12% the enemy's max HP per attack with this alone, even more if you sent them into negative MR with your penetration/reduction previously mentioned. This combined with the damage from your Q, E and repeated R should melt even the strongest tanks in a few seconds (it also kills super creeps really quick)

The point of AP Kog'Maw is to do ridiculous damage, while remaining out of range from your enemy.

Strengths

• Farm like an absolute boss (late-game you can kill entire creep waves with just your Void Ooze)
• Kill enemy APC, ADC or Support in 4-5 seconds without them ever being in range to engage you
• Best poke build in the game - NOTHING can out-poke a well played APC Kog'Maw, your ult has almost the range of a Lux ult, on a CD as low as 0.6 seconds. You can easily kill or harass enemies away from their own towers
• Very few counters, can beat almost any mid APC easily

Weaknesses

• Squishy as hell - is vulnerable to dash or teleport champions like Kassadin, Leblanc and Lee Sin
• If you get caught out you will almost definately die. Your only escape is flash, and the slow from Void Ooze. That said, a well placed Void Ooze can often save you or your entire team, don't waste it because it can turn the entire game around at critial points.
• Last hitting can be difficult for inexperienced players due to Kog'Maw's low base AD

Kog'Maw can destroy almost every traditional APC, like Annie, Ryze, Katarina or Ziggs. Play passively early, as your skills have low base damage at low levels. Focus on farming, and by the time you have your Living Artillery you should be able to poke your oppenent out of lane constantly.

He is also one of the few hard late-game counters to champions like Singed, Garen or Cho'Gath, you shouldn't focus them if there's squishies to kill, but if they're alone, you can lay down your Void Ooze to slow them, hit them with Caustic Spittle to weaken them, and then melt the **** out of them with your Bio-Arcane Barrage.

Help your jungler with their starting buff.

Depending on who you're up against, your aggressiveness can vary. Generally you should be passive until around level 4.

Focus on levelling Void Ooze and Bio-Arcane Barrage early, as the first gives you the most damage, and the second gives you some good utility (the slow his highly effective since it applies to an area over time rather than a single target, bypassing the effects of tenacity). Don't worry about Caustic Spittle as it isn't very useful at low levels, and the short range requires you to endanger yourself to use it.

Your pre-6 harass combo is to lay a Void Ooze on the enemy, then attack them with Bio-Arcane Barrage until they run away. You can often zone or deny an enemy this way if they don't have an easy counter like Morgana's Black Shield or Fizz's Playful / Trickster.

Keep in mind that Void Ooze has a slightly longer range than the skillshot overlay indicates.

You usually won't get any early kills, but if you harass enough you should be able to break even or beat your opponent at the early farming phase. Use your Explorer's Ward on one bush, hugging that side of the lane, and use your Clairvoyance periodically on the other bush, unless your team needs it used somewhere else.

APC Kog'Maw actually has a fairly decent ganking ability. A well aimed Void Ooze can slow down and damage both enemies at bot lane, giving your allies time to catch up to them and while you nuke them with Living Artillery. If any escape, you can finish them off with Living Artillery.

You can also help your jungle get dragon fairly quickly, or take your/steal enemy buffs with your Bio-Arcane Barrage thanks to the bonus 100 damage you'll get each hit against it.

Once you have your Tear of the Goddess and Chalice of Harmony your mana woes should be solved. You should be able to dominate any lane you go to, since you can safely harass the enemy with decent nukes via your Living Artillery. Make sure you pace yourself, though, your mana will drop rapidly if you chain them too much.

This is where APC Kog'Maw shines. You should be able to take out enemy squishies with 4-6 hits of Living Artillery, which should be really easy since each hit slows them 15% thanks to Rylai's Crystal Scepter.

Once you are good at landing Living Artillery, your biggest concern is self-awareness. You need to make sure that you are a safe distance from enemies at all times, and you need to be aware of where you are. Because you can often hit targets so far away with Living Artillery that you can't see yourself, you're prone to being ganked and caught out.

Teamfights

Having an APC Kog'Maw on your team makes teamfights stupidly easy. You can whittle their squishier champions down to half HP (or sometimes even killing them or making them flee) safely before a fight even starts.

When a teamfight does break out, you should sit back and land 3-4 hits on the champion pile-up while everyone blows their abilities on each other. After most abilities have been used, you can run in, lay down Void Ooze on their whole (remaining) team, hit your target with Caustic Spittle and focus them down with Bio-Arcane Barrage and Living Artillery, as well as using Living Artillery to clean up any fleeing low health enemies.

If the teamfight doesn't go your way, you can lay down a Void Ooze and spam Living Artillery to slow down enemies and help your allies escape safely. If an enemy chasing your ally breaks off from their team, don't be afraid to take them on, with your full combo you should be able to melt even the tankiest of champions, there's been many times that I've liquidated cocky Cho'Gaths.