Quick guide to AD Darius. I usually only see people playing a tanky Darius which I don't personally like. I feel he is better played in a carry role scoring lots of kills for your team. Darius works best at top or bottom lane on Summoner's Rift, and Top on Twisted Treeline.

Pros
Easy kills
Farms well
Has a huge axe

Cons
Slow
No natural escape mechanisms
His passive makes the opponents mad resulting in QQ's

Greater Mark of Strength - Nice for some bonus attack damage
Greater Seal of Alacrity - Faster attack speed is good for killing pesky minions quickly
Greater Glyph of Alacrity - ^^^^^^
Greater Quint of Might - As game progresses, this rune snowballs giving you more AD each time you level up

Offensive masteries to do more damage, life steal, critical strikes and armor penetration.
Standard build for most AD carries

Utility runes for speed, less time spent dead and faster recall.
The speed is to help chase down a wounded enemy, help allies, and get around faster, obviously.
The less time you spend dead, the more time you can spend carving up your enemies.
Faster recall is just a personal preferance.

What do I start with?
Starting with Doran's Blade gives you a nice health boost, extra attack damage and a bit of life steal. Alternatively, you can start with Long Sword and a few Health Potions.

Next is the boots.
Berserkers Greaves gives you more attack speed, and the standard Movement 2. Alternatively, Boots of Swiftness gives you enhanced movement 3 but nothing else, these help you move a lot faster.

Half way between early and mid game (around 10 minutes) you should work on the next item.
I like to go with Phantom Dancer. It gives you what you need, Faster movement, critical chance, and attack speed. No alternatives, just too good to be replaced.

Mid game
Now we need an item to do some serious damage. My personal preference is Infinity Edge. The damage it deals is amazing, and it gives you some higher critical chance. Its a MUST have for an AD champion. Alternatively you can get The Bloodthirster. It gets a stack each time you kill a creep (capping at 40) and gives you bonus AD and lifesteal.

Mid-Late game
Second Phantom Dancer time!
The more the better!

Late game. Around now you should be running out of item space, so you can sell your Doran's Blade.
We definitely needInfinity Edge if we went for The Bloodthirster. Alternatively The Black Cleaver or Frozen Mallet can be bought.
The more damage the better :D.

End game.
By this stage you should have around 15 kills and be up to the nexus turrets.
Buy a third Phantom Dancer, or another Bloodthirster.

Darius' Passive is Haemorrhage. Each time you strike an opponent they get haemorrhage stacks (capped at 5). Enemies with the stacks take damage over time per stack. For each enemie with haemorrhage stacks, darius gets faster, hunting them down.

Firstly we must must MUST get Darius' Q, Decimate. Early game this gets you kills. Mid game this gets you kills. Late game this gets you kills. Its extremely good and should be maxed out first.

After getting 1 point in Decimate , we need his E, Apprehend. This is amazing, and starts off almost every combo dragging your opponents to you. It passively gives you armor penetration which the enemies wont be able to prepare for and wont suspect it.

After 1 point in Apprehend, we need 1 point in Crippling Strike . This isnt the best ability but its not bad. After activating, Darius' next basic attack does bonus damage and slows the enemy. It should be maxed last.

Finally, Darius' ultimate, Noxian Guillotine . If an enemy is on less than 300 HP, you can take them from the air, as Darius leaps to them and slices them up. If you kill an enemy with his ultimate, it refreshes allowing for another. Pentakill anybody?

Flash is a must have. Allows you to catch up to enemies to deal the final blow, allows you to pass through walls to stop from dying, and allows you to tower dive (I dont recommend tower diving).

Ignite is a personal preference. Mainly for early game. Alternatively can be Teleport, Heal or Exhaust.

After buying Doran's Blade, we run straight for top, unlocking Decimate on the way. Harass and farm until you can afford Berserker's Greaves. During late game, people will buy armor to counter you seeing as you dont buy armor penetration, little do they know, your E passively penetrates armor, and you have armor pen masteries. Around level 16 you will need to get baron. Right click, Q, right click, W, Right Click, Right Click, Q etc. WARNING: Dont try to solo baron :c

The standard combo for an enemy at 3/4 health is: E, W, Q, basic attack, R
You must remember this.

Tips and tricks.
If an ally is getting chased, run behind the enemy and use Apprehend. This will save your ally and will probably secure you a kill.
When in team fights, dont initiate combat, wait for someone else to, and use Decimate as your first attack to get those haemorrhage stacks on and get some easy assists.
Traveling in packs of 3 or more you will almost always get all the kills being the awesome axe wielder you are.

This was my guide to an AD Darius. This is my first guide so I am open to advice.
Have fun slicing people in half.