Cho'Gath is a versatile champ that can be built in a variety of ways, or more specifically, a bunch of different builds seem to make sense when you just look at his skills. Many people opt for a tanky AP caster, possibly like Amumu. But who scares you more? Amumu or Cho'gath?
Most people will answer Amumu, of course, even though they may have nearly identical builds. We must be building Cho'gath wrong, because Riot makes sure it balances champions, right? Right. And from a lot of playing and some thinking, I believe that the optimal build to deal damage and tank is one that utilizes Cho'gaths Vorpal Spikes and health from his ultimate.
His main damage dealer, Rupture, is too unreliable to build him as fully AP, and his Feral Scream is too weak. If you don't build him with basic attacks in mind, then his Vorpal Spikes will be pretty useless, too. Which brings us to this build, a tanky DPS with ability usage (sort of like Yorick, maybe).
This is meant to be a top lane guide for Cho'gath, but the build itself could work if you are going mid, bot as support, or jungling, with a few modifications. Whatever position you are going to play in this first phase of the game, this build will yield the best results later on in teamfights and such. Just think of him as a hybrid, tanky, DPS melee champ with good roaming potential. Because that's what he is in this build.

I have 5 builds up there. The first is the main one. The next two illustrate some alternate items, the fourth is extra tanky, and the last is damage output oriented only. Don't do the last one, though. I just did it to show the offensive item options. The fourth build is pretty viable, though. You will be very tanky with your Feast stacks and over 200 armor and magic resist, and the Trinity Force will still allow you to do some decent damage.

Let's check out the good and bad of Cho'Gath with this build:

Pros:

• Tanky, but capable of large amounts of damage output
• Very fast from Trinity Force and Force of Nature (excellent roamer)
• Doesn't fall off late game
• Good in teamfights
• Good in one-on-one battle
• Good at excaping ganks and bad teamfights
• Excellent against mages, ranged ad carries, and melee champs

Cons:

• Less effective poke than AP Cho'Gath
• Relies mostly on Feast stacks for Health
• Not the best at catching fleeing foes
• Skills are hard to hit when not in melee range with enemies
• Prone to being focused in a teamfight, especially when max size

That's about it. I would say that the pros are more than worth the cons, though, and with enough skill, one can correct most of the cons.

The build listed above is, I think, the best in most situations. But it's never one build fits all. Let's take a look at some alternative items that still fit the idea of a bruiser:

Recommended:

Mercury's Treads
Contrary to some peoples' beliefs, Cho'gath is actually one of the faster champs. He starts with 320 movement speed, he only seems slow when you get multiple stacks of Feast and level up. When you get big, your foot steps get longer and slower, so you feel slower. But you aren't, so don't buy Boots of Swiftness. You especially don't need them with a Trinity Force and a Force of Nature build. Replace these with Ninja Tabi if you think they're a better choice that game.

Trinity Force
This is the source of pretty much all the damage output of this build. Most games won't get late enough for you to build damage output items besides this. I would say, ALWAYS get this. And usually, unless you are getting nuked to the floor, complete it first.

Frozen Heart
Pretty much all teams that you face will have physical damage, and most will have more than half their damage output in it. AD carries and most top laners and junglers will be dealing predominantly physical damage. Get this item, every game. It also helps with damage output, the cooldown reduction helps you get out your abilities and sheen proc. The mana will help with sustain, since Cho'gath is always mana hungry. I would say this item is usually indispensable.

Force of Nature
Most teams will have some magic damage as well. Force of Nature will go a long way to mitigate that, but it isn't just a defensive item. The movement speed bonus, when combined with Tri-Force, really makes Cho'gath a great roamer and better at chasing and escaping. This is very important after the laning phase.
However, I wouldn't say get Force of Nature every time. If the enemies only have one caster that isn't a big threat, I think it would be quite reasonable to bypass this one. Perhaps get some more armor or damage output.

Wit's End
I mostly get this as an offensive item. It grants some magic resist, which is nice, but mostly I get it for the extra attack speed and damage. What damage? Well, the 42 extra magic damage is pretty much equivalent to attack damage. So Wit's End is an item with 40% attack speed, 42 points of damage, and 30 magic resist that increase to 50 with your basic attacks. And it only costs just over 2k. Compare this to Black Cleaver which costs 700 more and gives you starts that are hardly better, and its an amazing bargain. Don't give this one up, even if they have hardly any magic damage.

Hextech Gunblade
This is a late game luxury item, of course. I think the spell vamp and lifesteal sounds and works good, but I hardly ever get this far to try it out. I still recommend it, if you get that far, but don't even start building into it until you have one item slot left.

Alternatives

Randuin's Omen
This could be a replacement for Force of Nature, if they have no magic damage. It could also be an item you opt to get instead of that late game luxury item, if you want to be tankier. If you are going to get this, make sure you get the Heart of Gold early game, to take advantage of the money it gets. It should pay for itself by the time you are prepared to build into Randuin's. It also has a pretty sweet active for team fights.

Madred's Bloodrazor
I really, really like this item. But, it's so damn expensive and it's only for damage output. You already have Trinity Force for damage output. However, it might be a better item than Hextech Gunblade or even Wit's End, after you build those defensive items. If the enemy team gets tanky and they seem to never die, this item can help melt their health. Definitely a viable replacement, if you have the cash.

Rylai's Crystal Scepter
This is ok. And yes, Cho'gath's Vorpal Spikes do indeed proc the slow, with a reduced effect because it's technically area-of-effect. This doesn't interfere with the Phage passive on Trinity Force either, so it will stack on top of that slow. It doesn't give too much health, so it won't be overkill when combined with the stacks on Cho'gath's health. This is a good option if you want a little more tankiness and AP to increase your poke power.

Abyssal Scepter
This is a replacement for Force of Nature, if you want more damage output and don't care about losing some speed (or that nice health regeneration). I wouldn't get this item to replace Wit's End and I wouldn't get it if you already have a Force of Nature. That would be magic resist overkill.

NOT Recommended:

Thornmail
Some people say this is a good item if their AD carry is fed. Personally, I think Frozen Heart is much better. The one extra point of armor won't block much, and Frozen Heart has an aura that reduces their attack speed. Also, the cooldown reduction will enable you to do more damage than the passive on Thornmail will.

Rabadon's Deathcap
Let's just use this as a representation of classic AP carry items. This is not an AP Cho'gath build, only some incidental AP is useful. In fact, I clearly said AP Cho'gath was bad in the introduction. Don't get them unless they give some other vital stat when combined with AP, like Rylai's or Abyssal.

Warmog's Armor
Items that grant a significant amount of health are a waste on Cho'gath. You should be keeping yourself at or near full stacks on Feast if you are playing well, so extra health beyond your masteries and Trinity Force shouldn't be necessary. Your ultimate gets you 900 extra points, you end up with 3200 or so once it's upgraded to level 3. Trust me, getting Warmog's on Cho'gath is something I did when I was level 5 and only played bot games. By the way, Cho'gath is the first champ I ever bought, so that is a true statement.

Moonflair Spellblade
Yeah. Derp. You are already getting Mercury's Treads, anyway.

Let's start with the runes. I'll be brief, because their pretty self-explanatory. Magic resist and armor, because Cho'Gath needs to be tanky, of course. I opted for attack speed instead of damage, ability power, or armor/ magic pen for several reasons. First off, Cho'gath should be getting enough damage out of his vorpal spikes and wits end, so he doesn't need attack damage.

Also, like I said before, AP is too unreliable of a damage output on Cho'gath to invest much in it. And I didn't get the penetration runes because Cho'gath splits his damage between physical and magic, but with a little more magic. And runes of destruction grant more armor pen than magic, so it doesn't quite balance right with him. Again, he has enough damage output without this, attack speed will truly optimize his damage output. If you want to tweak the build a little, though, you could change the marks or quints. Runes aren't game changing like items, anyway, they mostly are important early game.

Choices:
Glyphs:
Greater Glyph of Scaling Magic Resist
-Get that extra magic resist for late game.

Seals:
Greater Seal of Armor
-Armor for early game, when you have less armor than magic resist.

Marks:
Greater Mark of Attack Speed
-I think Attack speed optimizes Cho'gath's damage, so this is the first pick.

Greater Mark of Precision
-This will give you both magic and armor penetration, both which are beneficial.

Greater Mark of Magic Penetration
-This grants more magic pen than Destruction, since Cho'gath deals slightly more magic damage than physical.

Quintessences:
Greater Quintessence of Attack Speed
-Again, Atttack Speed optimizes Cho'gath's damage.

Greater Quintessence of Precision
-Get that armor and magic pen.

Greater Quintessence of Magic Penetration
-Only magic pen, which balances better with Cho'gath's damage.

Greater Quintessence of Cooldown Reduction
-Cho'gath won't be getting quite to the 40% cooldown reduction cap, he will get to around 32%. This gives and extra 3 or 4. Cooldown reduction is very useful on Cho'gath in both a battle and in between teamfights. Whenever you die, you will need to get 3 more stacks on your ult, and having a cooldown of 40 seconds or so means you will be ready in two minutes for another teamfight.

I recommend a 9-21-0 mastery tree. Again, Cho'gath should be tanky. The reason I went for the AP in this case is because we want the cooldown reduction. With this, Enlightenment , and Frozen Heart, you can get pretty close to the 40% cap. Magic pen is nice, too.

Grab Rupture at level one, because it deals a lot of damage and is good for both catching and escaping enemies. After that, grab Vorpal Spikes and Feral Scream, then, then max the spikes out first. If you want, you can level Rupture up a bit instead of rushing Vorpal Spikes to level 5, but I wouldn't up Feral Scream until the very end, because it is a weak spell with increasing costs, and Cho'gath is very mana hungry early game.

Now let's take a look at why this skill sequence is the best and how to use Cho'gath's abilities.

Carnivore
This passive is really only useful in the laning phase. When Cho'gath kills a unit, it restores a good amount of health and a small amount of mana. This is not the same thing as lifesteal, it only works if you last hit. While it won't help in most fight situations, it will help restore your health and mana when you are last hitting.

Rupture
This is your main active skill. While it is one of the toughest skill shots in the game, there are many uses for it, any where from catching an enemy that is running away to getting away from enemies yourself. You can also farm and poke well with it. Watch out though, it costs a lot, especially since Cho'gath only starts with 250 mana or so. In a fight, it works best when you are in melee range of the enemy, then place this right under their feet. You can keep attacking them while they are knocked into the air.[/b]

Feral Scream
This is a skill that is often overlooked, and for a good reason. Its weak and has increasing mana costs. The silence is useful, though, if you are laning against a champ that is relying on their abilities. You don't need to upgrade the skill for the silence either, it lasts 2 seconds at level 1.

Vorpal Spikes
This is your main skill. Its a toggle that adds an extra effect to your basic attack: you launch spikes that deal extra magic damage to enemies in a line. This effectively adds an additional 80 points of attack damage to Cho'gath, plus about a third of your AP. Because we are building Cho'gath as a tanky DPS, we want to up this one first. This skill doesn't affect turrets, though, and it might accidentally hit a champion, causing the turret to target you. Moral? Turn the spikes off when you are attacking a turret and an enemy champ is nearby.

Feast
Your ultimate. Aside from just dealing a large amount of true damage on a short cooldown, it also adds stacks of health to Cho'gath, up to 6. As soon as you get your ultimate, I would recommend eating minions only, just to get that health. Just keep on eating minions until you get to full stacks, unless you see an opportunity where you might be able to kill a champ with it. Once you get to 6 stacks, you can use it on an enemy champ anytime you like, you don't have to use it as a finishing blow like Darius's Noxian Guillotine.

Let's talk strategy, bub.

First off, laning. This guide was mostly intended for top laners, but it could be used mid, bot, or in the jungle. Your primary objective is to farm. Don't push too far, of course. Last hitting is especially important on Cho'gath because it not only gives gold, but increases your lane sustain. I would try to play passively and not get into a real fight, just use your abilities to disrupt their farming. Only get into a real fight if you have your ultimate ready or a jungler ready for a gank.
When you do get in a fight, set it up with you Rupture. Let them engage and walk into melee range of you, then place it just under their feet. Get some basic attacks in, then silence them so they can't effectively retaliate, unless they are Tryndamere or maybe Jax. You want to use Feast as a finishing blow in fights in a lane, or else the enemy might start to run when you suddenly devour a massive chunk of their health. Advanced tactics include killing their minions with your abilities AoE while fighting, to suddenly restore health with your passive. If you have to run, use your Rupture to get away. It's a good escape mechanism if you aren't too obvious with you placement.
In teamfights, try to catch enemies out of position with your Rupture. It's also the main poke you can use, since Feral Scream is a pretty short range. However, Cho'gath isn't the best champion to engage. While he is tanky, he isn't the tankiest, and doesn't have any really good escape mechanisms or moves to keep him alive and useful when he really should be dead, like Tryndamere or Olaf. Wait until the teamfight starts, deal large amounts of damage with your AoE and basic attacks.

Playing with Cho'gath is pretty intuitive. The main thing is to build him the right way to optimize his effective health and damage. If you got this far, good for you, and thanks. Try the build out a few times before you vote this up or down, please, and leave comments on suggestions that you may have. After all, I'm not the expert on how to play Cho'gath or anything, and this is the first build I'm making. I would like to thank JhoiJhoi for the start up guide she made, and while I know this guide is a long way from looking great, it would look worse if I hadn't read her guide. I'm going to continue to expand this guide, especially if it gets upvoted a lot. I plan to add a section about matchups: who Cho'gath is good against and how to play against the various champs you will meet top lane. I'll also upgrade pre-existing sections.

Finally, I'm done. That took longer than I was expecting. Now go play Cho'gath.