Dreadfully Akali, Strong power and Brave were within her.
Only the strong one will survive in battles, the brave will only die.
But She is Strong and Brave, fear no nightmare, because she will be the Nightmare!

Introduction

Akali is a nightmare to all other champions, she can easily take down anyone that she doesn't like. Akali is a speed melee fighter just like Yi, using a skill to get close range, tearing enemy apart, keep hearing screams from them til they die.
Akali is a champion with a few of item choices, as long as the core item is there, she will kill. Akali - Fist of Shadow, With core items, no such things as bad guide, it just the way how u play. Dreadfully Akali: "Don't TROLL with me! Harass me if u are able to kill, don't try harassing if you couldn't kill."

Pros:
-Easy farming
-Nightmare Assassin
-Strong burst
-Enjoyable (Looking at how Noobs fear you)
-*You can hide, but you can't Run* by Akali

Cons:
-Disable
-Squishy if you are a noob player. (When it Akali, no one can be thicker then Akali)

Abilities
[*] Twin Disciplines:
Akali's passive is what makes her a viable hybrid. She gains bonus magic damage from AP and spell vamp from AD. With AP runes+3/3 Archmage's Savvy and AD runes+3/3 Brute Force, both buffs will be activated at level 1.

[*] Mark of the Assassin:
This is Akali's main damaging ability. Use it well, use it once, enemy team players will be crying. Use this skill with a normal attack, enemy will drop tears for sure. (Late game or you are fed, just this skin alone can instant kill Squishy champions.

[*] Twilight Shroud:
This is Akali's stealth ability, which gives enemy fear.("I can see you, but can you see me?") With this skill, you can easily fear your enemy and starts with the massive burst on them. Not to mention, this stealth increase armor and magic resist and also gives enemy slow.
I max this right after Mark of the Assassin, as i can rapidly use this to either escape or kill.

[*] Crescent Slash:
In my guide, in my opinion, this is the useless ability that i never uses it even in Rank game. It cause way too much Energy and it isn't really painful, i would rather have Twilight Shroud as i can spam it fast enough to escape or kill. (With Mark of Assassin, this skill is totally useless, it cause energy low and miss kill, just save up the energy and keep bursting with Mark of Assassin just like how Leblanc does(bursting with her orb).

[*] Shadow Dance:
Akali's ultimate is what defines her. You can do so many things with this ability. Start off a surprise gank with it, last hit that about to die creep, chase and kill steal like a pro, burst with surplus charges, and most importantly, juke. Does a surprisingly large amount of magic damage.

Burst rotation, Q > R > Attack > Q > R > Attack, just with Mark of Assassin and Shadow Dance, it deals burst damage and is already enough to kill.

Summoner Spells:
[*] Flash [*] Ignite
Flash is a must, ignite is to easily get kills.
If u think exhaust is much better, you will troll Akali. Akali have Rylai to slow enemies and there Red Buff to slow enemy too, exhaust is definitely not a Smart choice.

Masteries:
What best are best, is there a need to explain?

Runes:
Isn't correct? You should know it too since you are a LoL player.

Core Items:
[*] Rylai's Crystal Scepter it helps to slow enemy and gives hp, it a must for Akali
[*] Hextech Gunblade it gives lifesteal and spell vamp, this is also a must.

Firstly, let me explain why is Xalrons, i lazy to explain this part as you have to learn though experience and not just by reading and understand how to play, i copy paste from Xalrons's Akali build guide. I think his guide is awesome too, i was using his guide when i first started playing Akali. But i make my own guide cause, to me, Akali is a nightmare to other people, i want people to feel fear whenever they see my Akali. (Guardian Angel is awesome Item for late game, but i didn't encourage to get it because, like what i said, Akali is a nightmare, why does she die? Anyway, here Xalrons's Akali Guide "http://www.mobafire.com/league-of-legends/build/akali-ready-and-willing-44394"

Sorry Xalrons for copying this part without informing you. You should know that Mobafire requires you to type a minimum of words. i am lazy to do it, just wanna share with others my akali guide. Sorry Xalrons :/

Early Game
Any lane works for Akali, though a solo lane is the best idea as Akali gets real strong with levels. Start off with your Boots of Speed and x3 Health Potions (or x4 if you wait at spawn). Boots are useful for last hitting without getting chased down. Try to keep your cool early on and don't engage unless you have to. Most ranged champions can hit you easily without repercussion. Use your Q to farm without getting harassed. Use Twilight Shroud for more safety while farming. This can also zone enemies away from their creeps and you can punish them if they get too close with a quick Q + auto attack. If you can secure a kill using Flash to proc a mark, go for it!

Your next two items will be Hextech Revolver followed by Null-Magic Mantle. Also get some Sight Wards to protect your lane.

Edit: Since the Hextech Revolver nerf, I have become very fond of skipping it and rushing straight for your Rylai's Crystal Scepter. Having a Rylai's around level 10 can truely turn the tide for your team in early fights! I will keep the Revolver as an option for if you are struggling in lane, but I much prefer and recommend getting Rylai's as fast as possible, possibly even before finishing a boots upgrade.

I strongly recommend Mercury's Treads, as crowd control is Akali's biggest weakness. Getting a Void Staff makes up for the lack of Sorcerer's Shoes. Ninja Tabi can be good against strong physical damage teams and goes well with Nimbleness in the Defense tree and Dodge seals (if you're playing ranked, you can always change your setup depending on the enemy team composition).

Mid Game
Your first completed core item is always going to be Rylai's Crystal Scepter. Try to start with the Giant's Belt. Rylai's is just too perfect for Akali. +80 AP, 500 Health, and ability slows? Absolutely necessary. No Rylai's, no Akali. Your job mid game is to attack any low HP targets and help slow runners for your team. Pop your shroud if you are in danger or get targeted. Be on the constant look out for Oracle's Elixirs for the rest of the game, as you have to play a lot more carefully if the enemy has it.

If you are going to want a Mejai's Soulstealer now would be the time to get it. I personally don't take it because, well, it's a risk, and you might not get any stacks. If you go this route, it can help to go for a Hextech Gunblade or Guardian Angel next for more durability instead of the usual Rabadon's Deathcap or Lich Bane.

As you head into late game, work towards your Needlessly Large Rod for Rabadon's Deathcap. I choose this item over Lich Bane because I feel it gives me a little bit more burst and doesn't waste the gold on a mana crystal.

Edit: Since the Rabadon's Deathcap nerf, Lich Bane is slightly more appealing. I honestly don't know which of the two is more potent, and I find myself switching between both. See the next section for more details.

Late Game
Why not get both a Rabadon's Deathcap and Lich Bane? Well, there are other items that are more important than just having pure damage. I usually want either a Guardian Angel or Hextech Gunblade and there isn't the time or gold to get both a Deathcap and Lich Bane beforehand. Then, a Void Staff also needs to be thrown in there! So, Deathcap or Lich Bane? It depends. Basically, I have two different builds that I switch between. It very much depends on your role on the team, the enemy team comp, and what the enemy team builds.

For example, if I know I will need to get a Guardian Angel very fast (usually against AoE ult teams), I might build Merc -> RCS -> Lich Bane -> GA -> VS, Lich Bane being the better option here because I don't have that much AP to benefit from the Deathcap. If I know I will need sustainability in long team fights, I might go Boots -> Revolver -> Merc -> RCS -> Deathcap -> Gunblade -> VS. The important thing is that you be adaptable. I don't normally reach a 6th item, but it would either be whichever I didn't get between the Deathcap and Lich Bane (if you need more damage) or Gunblade and Guardian Angel (if you need more survivability), or one of the items below.

Banshee's Veil is a situational item you might want vs. combo champions like Anivia, Blitzcrank, Leblanc, Morgana, Pantheon, Rammus, Ryze, Singed, Sion, Swain, or Veigar. Some other options are Zhonya's Hourglass (for champs with ranged stuns or slow moving projectiles like Brand's ult or Karthus's ult), Quicksilver Sash (for Malzahar ult or Warwick ult etc.), or Will of the Ancients if your team needs one. Of course, if you really need one of these items, you can always get it right after your Rylai's Crystal Scepter.

Team Fights
Don't dash into a group of enemies or they will focus and kill you. Single out lone squishies after enemies have used their first cooldowns on your teammates. Hit and run if they switch focus to you. Never be the first one to engage in a team fight. Wait until the tank's engage and the enemy team has their sights on one of your teammates. Then pounce their squishy and roll face, hard. Don't just stay in the thick of things if you are under fire. Hit and run. AoE abilities will kill you fast. Keep your Twilight Shroud and Flash ready for any emergencies, making sure there aren't any Oracle's Elixir out there.

Your priority targets should be low defense high damage enemies with little to no hard stuns or silences. Perfect examples are Ashe, Ezreal, Heimerdinger, Karthus, Kog'Maw, Yi, Miss Fortune, Nidalee, Sivir, Sona, Soraka, Teemo, Zilean. You should be able to kill them so fast their teammates have no time to respond. Wait a few seconds after the team fight starts, and jump their squishy using the following combo: R -> Q -> Mark auto attack -> E -> Q -> R -> Mark auto attack -> E -> Q -> R -> Mark auto attack -> E. Use Twilight Shroud/Flash to avoid getting focus fired. You have to be aware of the entire battle and everything going on around you! Constantly watch champions with hard CC, if they use it on a teammate, it is a lot safer to engage.

If the enemy team has Oracle's Elixir be careful about engaging enemies such as Cassiopeia, Fiddlesticks, Kassadin, Leblanc, Lux, Malzahar, Morgana, Ryze, Sion, Swain, Tristana, Twisted Fate, or Veigar. They can CC very effectively and wait until their team comes to kill you. If you know you cannot retreat, do as much damage as possible! It can be OK to sacrifice yourself to win a team fight.

Things to remember
1. Last hit only and don't push lane, harass and zone enemies.
2. Delayed Mark of the Assassin double activation to burst.
3. Try to buy a health pot and a ward every time you recall, AP elixir before big fights.
4. Gank often. Then push and/or do dragon. Proc push with Lich Bane (if you buy it).
5. Juke with Twilight Shroud and Shadow Dance.
6. When 1v1ing, kite around shroud, use double mark hit combos, be a ninja!
7. Don't start team fights or stick around if you get targeted, use hit and run tactics.
8. Whenever you see an enemy champion check for Oracle's, abuse shroud when you can.
9. Twilight Shroud, Flash, and Z-hourglass (if you buy it) for emergencies.
10. Kill lots of squishies.

Conclusion
Hey, Dread here, this part is mine. lol
Good Luck, Have Fun bullying, Nightmare isn't just Nocturne, Akali is the nightmare in the shadow world.