This guide is not finished yet! If you're thinking of downvoting just because it lacks detail, then please don't. Its not done yet!

Darius is an Attack Damage based character. His passive is a DoT that feeds off his AD aswell. The passive can stack, meaning more damage over time. But theres another good reason the stacking passive improves Darius's output. His ultimate has increased damage based on the amount of stacks on the target. The passive can only stack 5 times. Now that you know the whole "passive" stoofz, time to move onto how to play him. If you can reach somebody without them getting far from you, initiate with your Decimate, then into Crippling Strike. This will slow your target enough for you to be able to get a few basic attacks in. As he is running away, use Apprehend. This pulls any neutral or enemy unit, in a cone, towards you. This can PREVENT escapes AND prevent chases. If you take Exhaust, and have it ready, Exhaust somebody after you Apprehend them, unless you know they can get away.

Oh, another thing about Darius's ultimate. It refreshes if it KILLS someone. This means you can rack kills in!

If your ally is being chased, and you're RIGHT THERE, and easy thing to do would be to Apprehend the chaser. Not only will this save your ally, it could possibly get you a kill! But don't risk your own life if you're low health. You're a carry. Not a tank or a support. Unless you're saving someone who is more fed than you, save your own life before your tank's or your support's.

Lets start with viable Summoner Spells.

Here is a list of viable spells, and why.

Ghost - Increased Movement Speed, and you can't collide with units. This is never bad.
Exhaust - Perfect for "After I Pull-You In." Lowers armor and movement speed.
Ignite - Corresponds perfectly with your passive. This will not only improve damage, it will also reduce any healing.
Teleport - Back to lane fast. You can also teleport to save a teammate/tower
Flash - For when you want to pull someone, but you can't get to them without them running away and ****ting their pants.
Heal - This is a good lifesaver. Not only for you, but for your teammates, too.

Now for spells that kind of work, but aren't as great as the ones above.

Surge - Meh. You won't be using ability power much, but I guess the attack speed helps your passive out just a bit.
Cleanse - Gets rid of CC and reduces the next CC effect by 50%, but not really as useful as the others.
Smite - I guess jungling wouldn't be hard on Darius.

Now for spells that are absolutely bad for Darius

Revive - No. Just no.
Clairivoyance - This is for supports or people with sniping moves like Ezreal, Ashe, Lux, and Ziggs. You can take it, but it won't help at all.
Promote - Again, this is mainly for supports so they can earn gold.
Clarity - Yes, you eat mana early game, but this falls off bigtime late game and just becomes an unused spell. Go get a Blue Buff instead.

Alrighy. Now for the items..

Why no Trinity Force? Sure, its a great item, but the passive is wasted. It DOES NOT effect your W. AT ALL. Trust me, the other starts are SUPER AWESOME, but you might as well get a Phantom Dancer instead. It helps your passive and Madred's much more than a Trinity Force would.

Why a Phage early? A Phage is a health and damage item. You can definitely say its a no-brainer for Darius. He has enough output without an early damage item like BF Sword. The Phage gives you enough damage to sustain your output AND health to sustain yourself. Your next item is a Bloodthirster, anyways. You won't be without damage for long.

Garen is an excellent finisher. His ultimate deals increased damage based on how little health someone has. This means you should target low healthed tanks with your ULTIMATE. Not in general. If a tank is low health, just get them out of the way with your ultimate. Now, on to the big picture.