Hey there! I'm a Nocturne main, and hopefully I'll be able to shed some light on him for you. This is gonna be pretty long, but I'm going to go into detail on his abilities more than you would get from a regular description and how best to utilize them.
He's an absolutely amazing jungler, but is heavily reliant on your own foresight, and on your team making sure to either follow up on you, or that you can mop up for them.
First of all, his single target sustained damage is simply off the charts, especially if you build Skirmisher's/Devourer on him. An an auto attack reliant champion he has everything you would want, and he can function as either an all out damage assassin or as an offtank, although he makes for a much better assassin IMO, and should only be built tanky if the team needs it, or if you're falling behind.
His passive is amazing for both duels and teamfights, and while it doesn't give a lot of health on hit later on in the game, it gives enough to assist you with clearing the jungle early on even if it isn't as good of a sustain as Warwick's kit or Lee Sin's spellvamp. Against a single target it'll give you an extra bit of damage every few auto attacks once you get some solid attack speed on him, and if you have it ready before ganking into the botlane or when there are several enemies grouped it'll take a large chunk out of them in one swipe. It's gotten me many a multikill.
Q functions as a sticking mechanic by boosting his speed when on a trail, as an AD steroid by boosting his AD when on the trail, and more importantly it allows you to track stealthed enemies! It has a very wide hitbox and a long range, but the movement for the missile is relatively slow so learn to lead it. It passes through enemies and will deal damage to all of them without any reduction, which makes it a teamfight terror when it's at full rank and you have a solid amount of AD. This ability also helps you with your jungle clearing by giving you extra AD, and this will interact with the 120% damage cleave when your passive is up. It goes through walls, which can be useful for sniping low health enemies who flash away to try and escape.
W will make or break you as a Nocturne. It gives you passive attack speed, synergizing well with his passive and the idea that he's an auto attack reliant damage dealer, and if you activate it to use as a spellshield and an enemy makes the mistake of using an ability on you, they get to deal with you having double the passive attack speed! This is the ability that lets you win trades and saves you long enough to take out high priority targets in teamfights. However, it can feel a little unintuitive at first because the shield takes just a bit longer to come up than you would expect. Just like his Q, you have to learn to lead his shield. People who know Nocturne well will have to make the hard decision when you activate it during a duel of not using any abilities for it's duration or risking doubling your attack speed by popping it ASAP and hoping the rest of their skills will get you. This spellshield makes it nigh impossible to lose duels against anyone who's not overly fed, and will stop any ult reliant enemies in their tracks. Fizz threw his fish? W. Darius has some stacks on you? W. Lux about to fiyah her lazar? W. It'll save you from a distance, and wreck up close.
E is the utility that gives you better ganks. It scales off of AP, so it'll deal very meh damage, but the fear is what you're looking for. The tether range isn't very long, a bit smaller than Fiddlestick's drain, but if you can keep them in distance by tagging them with your Q trail first you're rewarded with a few moments of retaliation free auto attacks. As an added bonus, the damage it deals doesn't aggro turrets until the fear goes through, so if you're going to turret dive make sure you hit them with this and just keep chasing them through the turret without actually hitting them. The fear will activate, they'll run out of the turret range, and you can then safely continue to apply the pain.
R. Oh my god this ult. It's the definition of ganking. At early levels it's range is long for an ult, but still requires you to be in solid positions along rivers or in jungles to actually use it to get to lane. The damage it deals is decent, but it's not going to instagib someone who isn't already at low health. But the tradeoff for having anaverage amount of damage? The range. Good lord the range. At rank two you can gank from a good portion of either jungle, and from farther down a lane than most will expect. At max range? You'll be supermanning clear across a map to dive on that poor fool who decided pushing the top turret alone was a good idea. This ability allows you to catch out opponents who are trying to go it alone, and to dive into the backline of a teamfight to take out an enemy carry before they have time to react. Make sure you hit your spellshield before you dive in, though. As an added bonus, when you use this the enemy team loses all vision. Their screen goes dark, they can only see a small distance around them, and they lose sight of their wards. They are entirely blind, meaning that ADCs can no longer provide any damage during a teamfight because they have no one to click on! Even if you can't get to a fight off of the leap, using this can help your team win it anyways by blinding the enemy and giving your team a distinct advantage for five seconds. Use it during a teamfight, but don't immediately use it to jump to the backlane, and you give your allies a few more seconds to deal damage to a confused enemy frontline before you dive in to kill the carries. When you hit your ult and their screen goes dark, every member of the enemy team gets worried. The carries wet themselves wondering if it's them or someone else, the low health enemies are clenching as they run for the safety of a bush, and the tanks are preparing to use whatever they have to to protect whatever carry is near them. It's a great mindgame, a great teamfight ability, and an amazing leap.
Hoo boy.
Your skill priority is R> Q > E > W. The skill order should be Q > W > E, then max Q, then E, then W last. Ult at 6, 11, 16. Your Q is your main source of damage, so it's a no-brainer. But why not max the spellshield first? Simple: the spellshield doesn't block any more or less depending on it's rank, and while the first rank gives 20% attack speed each rank after only gives an additional 5%. Your skill points are better spent on your E, which reduces it's cooldown, gives it just a bit more damage, but increases the length of the fear. That's what you're looking for during the midgame to help you take down single targets.
Nocturne has two build paths, assassin and offtank fighter. The former is widely regarded as the better, but in times of need the latter will still work fine.
You're going to want to get Skirmisher's Saber and the Devourer enchant. The on hit damage that these two will provide you is off the charts, especially after you start getting stacks quicker in your jungle and the enemy's, and getting fed off of assists or kills.
Next you will want to grab Boots of Lucidity. He absolutely needs CDR, as this will make his passive come up quicker, allow him to Q more often to keep his damage bonus and stick to targets, and most importantly it reduces the time on his ult. The tradeoff for how amazing his ult is comes in the cooldown. It starts off at about three minutes, so CDR is an absolute necessity.
After that, build a Brutalizer. He loves the CDR and armor pen, and the 20 AD is nothing to scoff at. But instead of finishing it, instead start working on either a BotRK or a Hydra.
The first is probably the better of the two as it has more synergy with his kit, providing more attack speed for more on hit procs, a nifty movement speed steal that heals you a significant amount, and allows him to mow through tanks. Hydra is a great choice if you're looking for more burst damage, but I usually wait to get it until later when the Cleaves passive/active will do more. However if your team is falling behind early, this can be a solid choice to help push lanes, clear your jungle faster, and provides a bit of quick damage when you go in on their carry as it resets his AA timer, letting you get 3 attacks in quicker than you could get in 2 otherwise. The Hydra is usually better for a tankier Nocturne since he can sit in fights longer to deal AoE damage. When I was first learning him I build Hydra first in almost all cases, but as I've gotten better BotRK really has been the better option, but it's up to you.
From there finish the Black Cleaver, the added health and damage, and the passive armor reduction per hit are great on him combined with the CDR.
After this you can choose to either build a BoRK if you built a Hydra, a Hydra if you built a BoRK, or start working on alternatives. If I'm doing really well I'll usually build my Hydra around this point, or at least get the Tiamat. If the enemy is already starting to stack armor to give you a problem, a Last Whisper fits in great here and between the LW and the Black Cleaver, carries are absolutely mush before you.
Around this time you should be fed. Very fed. It doesn't matter whether it's kills or assists, although chances are it's the former, right now when you show up lone enemies will run, and even if they're with a pal they still hesitate. The mid to late game is when Nocturne starts really hitting his stride and becomes a huge threat due to the range of his ult. Here you have two options: build a GA if the enemy team can lock you down if you make a wrong move and delete you, or build a Zephyr to be just THAT much stronger. Me? I prefer the Zephyr. 25 more AD, 50% more attack speed, along with 10% movement speed and another 10% CDR? You should be hovering somewhere around 250 AD at this point, with 35% CDR, and around 1.9-2.1 attack speed depending on your runes. There is no one who can duel you 1v1 and it takes a significant effort to fight you 2v1. This Nocturne was the one that got me my first quadra.
