Darius will probably be a solo top. But he can also jungle
If you go jungle, feel free to pick him any time, if he is not banned.
But if you happen to want to go top, try to last pick him, and only if you will do well versus the enemy top. No point first picking a Darius and they just pick a vladimir, or a teemo and completely shut you down.

If you are going jungle, you should probably pick him early, so the enemies might think you are top and counter you top, while your team will counter whoever they picked.

In laning, occuring you did not get counterpicked. Try to play passive until you get your combo (level 3). If you play aggresive before, this will happen:
1-You will not have any gap closers, the enemy might just throw a few spells on you and come out ahead.
2-You won't have the slow, meaning yo will do a little bit of damage and use mana, and loose some CS so the enemy takes 100 health.
3-You wont have much damage to win a trade.

Once you get to level 3, go in to last hit minions, he will be scared of you. But don't overextend, all players know not to feed darius, so they will be ganking you often.
Once you hit 6, feel free to push your lane, go ganking, steal jungle... If you get ganked, 1x1 you will usually get a kill and come out alive. 2x1 you might get a kill but die along. 3x1... in the case you were stupid enough to not see any mias and not have any wards, then you deserve to die.

In the case you get counterpicked. Play extremely passive, last hits only. Do not trade with him ever. Even if you think your ult will do short work. Because it usually doesn't against counters. Ask for ganks frequently and make sure you get fed/farmed before you start to get aggressive. Buy items which will counter your enemy.
Remember, most of your damage is base damage, dont worry about not buying doran blades, or other damage items, just get tanky to deal your damage and come out healthy.

Your jungling isn't great, but the ganks are usually kills for sure.
Your Q will push out most damage, but the W will give more utility in the case the lane you are ganking has a high damage dealer in your team. such as a burst mage or an AD carry with a great early game (Ezreal for example).

You will have to buy oracles elixir on darius, he is an Expensive jungler and can't stand around lanes waiting for ganks to maybe get a kill, he will fall behind this way. But don't rush yourself, take a HoG and a Philo stone so you can take sometime to wait, but don't camp around for minutes, while every other enemy farms.

Start at wolves, grab blue buff with help (do not use smite). go directly to enemy red, steal it if possible. Will be an easy kill if you do.
If you stole it or not, go gank bot if you are purple team, or top if you are blue team. don't take too long. then go back to wolves, wraiths, give your red to a teammate or take it if you weren't able to steal enemy's. Kill the stone brothers and wraiths again. You should have gold enough to get a philo stone, and the blue should be coming up. Give it to your mid if he is mana dependant, of give to your support or take it yourself.
Now proceed ganking and farming.

Your role is to be a tanky assassin. How? you ask me:

Your base damage is great, and you have an execution, this is all assassins need. People will try to CC you, this is why Mercury Treads and Juggernaut (mastery) and Banshees Veil are so important. So you can soak up their CC. You will have a spell block, and 45% CC reduction. You will still be focused by them, but remember, the more CC you take, the less your team takes. The less CC your ADC and mage take, the more damage your team does.
If the enemy chooses to NOT CC you, then they will regret for your damage. You will be pretty tanky, a threat and a indirect carry.
Doign all of these jobs is sure to win, by soaking CC, your team will do more damage. By being ignored, you will take out the main targets and win the fight. By being completely focused down, the enemies will be on cooldowns for the rest of your team. Don't be afraid to die, it IS your job, but to take a while at it. Dying to a annie combo alone will still loose the fight.

I personally prefer flash for being the besst summoner skill, offensive AND defensive. all champions take this skill for that. being able to reposition yourself for no mana cost, instantly, to both offense and defense is great.

I take heal for prolonged durability in fights, as long as saving people.

Ignite is also a great choice, though your ult is true damage, and you are supposed to execute with it, not leave the kill for ignite. If you truly need the heal reduction, the mid usually has a ignite, and you can ask the jungle/top/mid to buy executioners calling/morellos evil tome.

Exhaust is good, but one is usually enough in a team, and the support usually has it. I just feel that, you have a slow, and people won't face you 1x1. If the enemy is going to escape, he will do it exhausted or no. by a flash or another skill. There are better choices here.

Clarity, sure take it if you don't want to buy a philo stone and want to cast Q all day to farm. /sarcasm. Please don't take it, you are not mana dependant and almots any skill is better here.

Surge: No use for the AP and the attack speed isn't that useful for darius other than putting stacks a bit faster.

Ghost: Might help out in teamfights, though a shurelias will do the same and help you be tanky. It is a good idea to put this skill and trade shurelias for a Guardian angel, or an Aegis of the Legion.

Cleanse, I do not think it's needed on you, though with mercury Treads it WILL make you 100% resistant to CC.

Clayrvoyance, DO NOT EVER PICK ON DARIUS. I mean, darius can' realy support can he?

Teleport: Useful, not the best choice.

Promote: You don't want to push your lane do you?

The Range of your Q hitting with the blade is the same as of your pull. So try to always hit Q and then pull your enemy, so he takes the 50% bonus damage.

W resets auto attack timer. So cast it right after attacking once. This way you get a second attack a lot earlier than you would have normally.

Ult deals True damage, try to remember the damage it deals before the teamfight, when you see your enemy has low blocks of HP (each represents a 100) cast it to kill him.

Do not kill every single enemy you can, leave some for your teammates. If you get fed and they fall behind, won't be of much use.

In laning, your enemy does not know the cooldown of your E. So try tricking him into running away from CS. Always have a ward on key spots for his ganks. Zone him out by making him think you will pull. Don't ever use E unless it will hit. If he sees you just used, he will kite you and harass you and there will be nothing you can do.

Before you die, use your ultimate in the squishiest target possible, even if he has no hemmorhage stacks, your teammates will appreciate the damage.

Sometimes it is more worth it to cast your ultimate without killing, letting someone else get the kill, or Hemorrhage do it for you.

A mercury Treads, Trinity force, Randuins, and Banshees are must have on Darius.
The other 2 depends on what you need.

I usually take one bloodthirster to have that feel of dealing lots of damage, but instead you could become tankier.

Shurelias will help you get those grabs, and run after feeling enemies, plus helping out your team in a LOT of situations.

Force of Nature is a good choice also, but a late game threat to you is CC, and the AD carry damage. The regen will help between pokes and skirmishes, but not much use in the fight.

Frozen heart is a pretty solid item, though i feel randuins will do a better job on this champion. Along it gives a Gold per 10 item, which is very usefull for you.

Maw of Malmortius is pretty solid, but if a mage can get you this low, why can't he take 500 hp more? And the magic resist it gives is nothing compared to what a FoN gives or a banshees along with the shield component.

Atmas impaler gives too little armor, and after the nerf on the damage, it isn't enough for 1 item slot. It won't make you tanky, wont make you do heavy damage. All it will do is allow you more clutch crits, which Darius does not relly on.

Some could say boots of Swiftness is a good choice, though it will make a lot squishier for 20 more movement speed. It will help a lot in ganks, but not too much late game.

Mobility works pretty well if you are jungle, but as soon as laning phase ends, sell it, you won't be ganking anymore, and it provides nothing in the heat of batter, which darius is ALWAYS in.

Ghostblade:
Pretty solid item, but it will make you pretty squishy. And if you want armor penetration, pick a last whisper to add to your 25% instead. You will reach somewhere around 60%, a little less. Making 40% of enemy armor useless is nothing to laugh at.

Last whisper: This is a must have if you are doing well early game, since you are already filling your role, and the enemies start to counter you, buying this will delay even more the time they will be able to do so. Giving you team kills enough to carry, or come out ahead.

Warmogs: Sure, the health helps a lot, But armor and Magic resist are a LOT better than just stacking health. Early game it will help out, but when they start to get those 400-500 crits, you won't notice you bought a 3000 gold health item.

So... your job is to Die.

I am not joking. But not to straight up die, take your time at it, make them work for your death. Leaving you alive is a threat, And so is killing you if you are tanky enough.
Soaking upp all damage and CC gives your team free roam. being ignored gives YOU free roam.

Here is on thing thou shall never do. Don't EVER ult early and not get the kill in a teamfight. You are a threat because if they are low enough, you can just execute them. The moment they survive and the ultimate gets on cooldown, you can be ignored and not ba a threat to anyone.

And lastly, Darius is NOT overpowered. You have no escape, low mobility, no defensive mechanism. The only thing you have is DAMAGE, and lots of it. You are not the tank, but you take a while to kill.
People scream OP for having a True damage ultimate with refresh on kill. But let's take a look:
level 3: 340 (0.75 AD) True damage. High manacost. max damage: 680 (1.5 AD).

Olaf E lvl 5: 340 damage, low health cost (hardly seen with Vicious Strike activated), Very low cooldown.

Darius can only ue his ultimate ONCE in a person, dealing more damage. Olaf can use it many times in the same person.

None of the skills are OP, they are just different, along with the kits. Olaf is the duelist, the more you focus him, the harder he will hit, the more you ignore, the more True damage he will land.

Darius the more you focus, The faster he will die, but the more you ignore him, you will regret more than ignoring olaf.

Pros

A LOT of damage
Very tanky
Very fun to play
Great Ganks
Funny to see people complain you are OP
One of the best mid games.

Cons:

Falls of late game
Can be easily juked
Slow clear times in jungle
No escape
Useless with ultimate on cooldown.