You want to be the only Lethality user on your team and have at least one champion on the enemy team which 1. Doesn't have any escapes or 2. Does not build any armor whatsoever.
You then want to proceed by stalking that player all game to take the ideal scenario to ult him when he is either A. Alone and far from his teammates or B. With his team who have most of their defensive abilities on cooldown.

After analizing this proceed to do the following:

1. Farm until level 6 regardless of how many times your lanes ping you (Ignore their pings /fullmute all is highly advised) (You are win to win the game, not to listen to your teammates)

2. Take farm in lanes whenever your laners back (if they are going to miss CS). This is very very important.

3. Take enemy jungle if you are playing against a high ganking enemy jungler.

4. When you have ult proceed to ult the lane who has no escape or who has low defensive capabilities (often midlane or adc). ALways look for a gank when your ult is off cooldown.

5. Prioritize cooldown items early as it will surprise your enemy laners when they hear "DAARRKKKKNESSSS" every minute.

6. After kills, push the wave out and get damage on enemy turret. This is very important as you want to end the game during the midgame and not the lategame. (Nocturne falls off late game due to enemies purchasing items to counter you)

Playing from ahead is almost guaranteed you will get the victory as Nocturne snowballs game.
Playing from behind is very hard. You will need to be patient and wait for enemy mistakes to claw yourself back into the game. At low elo this is particularly easy to pull off as enemy adcs usually go to lane solo in midgame so all you have to do is ulti them when they do.

Bronze, Silver, Gold: You can always find an opening to get off your ultimate and get free kills.
Platinum: You will need to focus on getting vision. Focus on regularly buying pinks and get scrying orb to cast your ultimate.
Diamond: You will need to focus on punishing the enemy jungler when he makes mistakes to get your lead.
Master: You're good enough at the game to understand how to make use of his kit in this meta.

Use your Q to catch up with the enemy. Make sure to fight in the trail as it gives you a lot of bonus damage on auto attacks in early game especially.
Your W should be the first spell you use when fighting someone. The enemy will 99% of the time start fighting you by attempting to land his/her main skillshot/damage spell (Lee Sin Q, Lux Q etc). When your spellshield goes through you will get an attack spped steroid so fight him right after.
Cast you E almost instantly after you cast your spellshield to prepare to melt him with your "Lethal Tempo" and attack speed steroid granted from your W when spellshielding an enemy spell.

Late game, use your ultimate to midway through a fight. DO NOT USE IT TO ENGAGE or the enemy will just blow you up and you will be considered "Borderline inting". Wait until the enemy have used some spells or they make a positioning mistake and use your ultimate to punish it.
After casting your ultimate you can wait some time before launching yourself to the enemy. It is advised as this allows your team to prepare to follow up.
Your combo is R > Q > AA > W + E > AA > AA AA AA AA AA
The enemy is either dead after this or you should run and get the hell out of there as you have nothing else to kill him. No dashes when ult is on cooldown will mean you will get kited.

I'm a Nocturne One trick Pony since season 3 and was Master tier during the beginning of Season 7 and also being the Best Nocturne in the world during that monthly period.
Currently diamond 2 on EUW, Nocturne has not changed however there are much better jungle picks at the moment than Nocturne.