This build is more of a hybrid tank/Ap so if your against that I recommend using Cho'Gath as a pure tank with warmog's and leviathan.

The reason you should pick boots of speed as your first item is for chasing and running away early on trust me you'll be **** it a lot as him. I then usually go with 2 health pots and 1 mana pot because he burns through mana in the begging in about 3 abilities so you'll want that extra mana boost.
Cho almost always goes top he works best there. As Cho'Gath if you followed the runes right you should start off with a hefty amount of health. Which means you should be leading who ever with you into the bush, or if your soloing for a jungle character you should most likely play it safe and just stay around your turret. As Cho if you have a jungle you should always solo the 2 up top don't let anyone else do it. In my experience the gentlemen is the best solo champion in the entire game. Towards the end of this phase you should have feast by now and should start noming on minions whenever you can it is essential to have that extra health and use it as a nuke after you get your max feast stacks.

As of mid game you should have farmed enough to get your first main ROA which is in my opinion designed for cho'gath. The mana is a must have the AP will let you put out more damage, and the health is great for a tank!!!! What's even better is that you keep gaining all of that for quite a while. After you get that you should start to go into roaming/help mode. Which basically means go around and gank it up with usually mid. After that you should top off your boots by getting mercury treads which is a must have for every tank. Then you can start working toward a abyssal scepter or frozen heart.(depending on if they're heavy DPS or AP)

If by now they haven't surrendered to your awesomeness you should have rylai's crystal scepter and be working towards your last item the one that truly makes you invincible Guardian Angle. The only problem I have with Guardian Angle is that they're team seems to focus your more squishy team mates than you, so if you think that will happen I suggest going with Warmog's Armor. In a late game you should always stay with your team and be the first one to initiate a team fight with rupture and the last one to finish them off with feast and or rupture. Your feral scream ability is one of the most essential abilities in team fight you must use it after you pop your rupture to silence they're entire team leaving them open to your damage doers.

A trick I learned with him is to start randomly acting like you have a team mate coming to gank them, by acting super aggressive and pushing a lot after you pushed them back a bit fall back and repeat not to soon, but just when they're about to push into your tower. Cho'gath is also one of the best chasers in the game by rupturing ahead of time to where your enemy is running after you do that feral scream and then you probly should have them by now if not feast on them and make it a stylish kill.

Lastly Chogsworth as my friend likes to call him is one of the best farmers in the game. All you have to do to a minion wave is pop them up with your rupture and then feral scream BAM 150 gold. Late game however you only need to rupture and you got the entire wave.