Whilst some may question a full AP build on a champ such as this, it works because of the fact that Cho'Gath can still be very tanky, even without much Armour or MR. This is because of his Feast granting him more health if he kills an enemy unit or champion.

Rod of Ages is key, as it has a lot of stats that Cho'Gath highly benefits from (those being AP, mana and health). It helps as it adds to his already high HP stat after Feasting and his moves are not very mana efficient. The AP is quite self explanatory as to why it's there. It is a must have item on Cho, regardless of build, in my opinion.

Abyssal is another key item, as it adds more AP (the more the merrier) and also nullifies an opposing champions MR, making it easier for Cho to kill them with a Rupture, into Scream into Feast combo, provided they're squishy enough. Regardless, this combo should do lots of damage, because of the true damage done by Feast.

Deathcap is there due to it's high flat AP stat, making it a favourable item. Whilst it can be switched out for other items, such as Zonya's, we are looking to have insanely high AP with this build.

Lisandry's Torment is there due to (again), the reasonably high AP stat it gives and the +15 Magic Pen it gives. This, coupled with Abyssal can make sure not even champions carrying heavy MR will feel the wrath of Cho'Gath.

Morellonomicon is there more so for the CDR it gives, as is Athene's Unholy Grail. These are two items that give AP and CDR, both giving 20% CDR respectively, allowing you to win more fights, due to getting more abilities in. These are both helpful as Cho's abilities all have quite lengthy cooldowns (with the exception of Vorpal Spikes, obviously). The mana regen given by both also makes it very difficult to run out of it, coupled with the extra mana given by Rod of Ages.

At the start of the game, try to play passive as possible. Focus on farming, and only fight the opposing Champion if they engage first. Make sure that the river is well warded, so that you see incoming ganks and avoid them. You should try and use your E to kill low minions, and harrass enemy champions. Play like this until you get your Abyssal Scepter.

By the time you get your second item, you will have quite a high amount of AP. Nothing too insane, but certainly enough to poke holes. Use this to your advantage, knocking up an opponent with Rupture, and hitting them with a Feral Scream combo to deal damage and make them back off. You should try to not engage recklessly, as by this point you should still be building stacks of Feast. Use your Feast on minions and potentially the opposing Junglers camps to build stacks, as they are you're main source of tankiness.

Once you build Deathcap and have 6 stacks of Feast, you can feel free to engage enemy champions. You may be able to take certain Champions in a 1v2, provided they don't do too much damage. You're abilities should be dealing high amount of damage, and Feast should be able to kill most champs when they are around 1/3 - 1/4 of their max HP.

Once you get Lisandry's Torment, you should be dealing extreme damage, and even tanks building MR to stop you will feel the sting of your Q - w - R combo. You should be difficult to take down, by anyone short of a very strong assassin with good itemisation.

Morellonomicon and Athene's Unholy Grail will make you a very clear threat. With the max amount of CDR, abilities should recharge much faster, making chases easier to cope with, provided the enemy somehow lives to be able to run. Stick with your team so that you can both protect them and help them burst enemies down. Cho's AoE W and Q should be especially helpful for this, as they can slow an enemy enough for your entire team to focus and destroy them.

If you die at any point, resort to playing in a passive-agressive manner, only attacking champions if they decide to attack you. Focus on getting back your lost Feast stacks, as again, they are your main source of tankiness outside of Runes and Masteries, so they are important to keeping you alive and well.

Try to keep early game as neutral as possible, avoiding being killed if possible, and not aiming to get kills specifically. This build should require a lot of farming, as a lot of the items here are quite pricey. If you have an atrocious early game and don't get Rod and Abyssal done quickly enough, the enemy laner can easily snowball you.