Greetings.
Perhaps not many will like this build, some might find flaws but everyone has their own way of playing Akali and that is understandable.
What I am going to show you here is a full build and how to play akali using this build.
This build will require some defensive gameplay until level 6 (like most of akali's builds I assume) so if you do not like to play more defensive than offensive at first, then this build is not for you.

Pros:

-High damage when using skill combos
-Can join ganks but for a short period (some might focus her thus her health will allow you to take a few hits)
-OP late-game

Cons:

-Requires defensive gameplay early-game (until lv. 6)
-Might require some farming for gold sometime
-Easy to kill in a gank

Twin Disciplines is Akali's passive and it's self-explanatory. With every 6 AP you have, akali recieves 1% bonus magic damage to her standard hits and upon obtaining 20 AP (which you will start with if you have a full build) you will deal 8% bonus magic damage.


Mark of the Assassin should be the first skill you get since it is a ranged skill thus allowing you to deal a small amount of damage even from the distance. When you get up close and hit the target while this skill is still marking him/her then you will deal extra damage which will come in handy on no matter what lane you are on.


Twilight Shroud is better than most of the people think it is and this is a minus for them. This skill should be leveled at level 3 for it's capabilities such as concealing you from an enemy (unless they have wards or traps) or slowing down enemies that walk in it. If you underestimate this ability then you're as good as dead.
You may want to try and cast this on an enemy before engaging in melee combat with them (slows them down and in case of need you can hide inside it)


Crescent Slash is quite good if you're planning on farming multiple minions or you're dealing with more than one enemy champion. Even if you're 1v1 you can still use this as it will deal massive damage and with your spell vamp, you get some health back. Preferably used in combination with Mark of the Assassin.


Shadow Dance is a charming technique but it it has more tricks to it. It may serve as an escape tool or catch-up tool depending on the situation. If you're running from an enemy and you have enemy minions on the way back, you can use this to escape faster.

Here are some combos that I've been using and have been very successful so far.





You can at any time just combine your abilities in any matter you enjoy but keep in mind what each skill does.

So here is how you should start playing Akali if you're following my build...
First of all, make sure that you use the mark of the assassin as much as you can until you reach level 2. From there, continue with the combo: Mark of the Assassin + Crescent Slash and normal hits. When you reach level 3, you may (or may not, depending on the player) scare your enemies by placing a Shroud of Darkness on the battlefield and hide in it since low levels are weak most of the time. (Try to avoid doing that if the enemy has area damage such as katarina's ulti, riven's broken wings, alistair's stomping etc.)
Once you're level 6, the real fun begins. At that point, you may easily attack any champion using your ulti but make sure you're always having 3 stacks before engaging in combat since you never know when you need it.
From level 6 you may also continue building up your items and skills then use combos.

NOTE: Rylai's Crystal Scepter is quite vital for akali since it offers AP and Health enough to sustain some damage from the enemy so do begin with that.

A very brief description of the summoner spells...





First of all, Flash is a great asset to Akali if you want to catch up an enemy or escape. For example, Flash and Shadow Dance used in combo will allow you to catch a fleeing enemy champion even if it is a bit far away from you.




Ignite should be used on enemies only if you can't catch them and they're low on health or you have a hunch that you will not be able to kill them but still leave them on low health (you have no escape so you can only fight whether you die or not).

Greater Seal of Scaling Ability Power is a great rune if you're planning on building a lot of ap. Unlike Greater Seal of Ability Power which offers you a +0.59 ability power for each rune you have, scaling ability offers you +0.1 ability power per level (1.8 at champion level 18) for each rune. This means that you will recieve more ap late-game rather than early-game.



Greater Mark of Magic Penetration is a great choice if you're willing to inflict magic damage. This rune will offer you more magic penetration on every hit you perform on the enemy, making it quite valuable since it bypasses their magic resistance.



Greater Glyph of Scaling Ability is taken for the same reason why Greater Seal of Scaling Ability is, but unlike that rune this one offers +0.17 ability power per level (3.06 at champion level 18) which make it more valuable than the seal rune. I would strongly suggest buying these runes before the seals since they have the same price and offer more ap late-game.



Greater Quintessence of Ability Power is quite expensive, agreed, but with three of those runes, you will get +4.95 ability power multiplied by 3 (14.85 ability power to start with). Quintessences are quite expensive (1025 IP) but to start with 14.85 AP and the AP from the masteries could easily reach 20+ AP, better than wasting money on an Amplifying Tome and buying boots instead.

On the masteries, I will try to go briefly and I will start with the Offensive Tree.




Summoner's Wrath must be picked because it will offer you 5 AP and AD everytime when it's in cooldown.


Sorcery will offer your champion a 4% cooldown to start with so you can use your skills more often from the start.


Butcher offers you more damage against minions which will help you farm them faster since you will be needing that early-game.


Blast, like the scaling ability power runes offer ability power with each level. You may think of it as 4 custom scaling ability runes with 1 AP for each level.


Arcane Knowledge is great since we're going to have some magic penetration. This mastery will add a bit more to your magic penetration runes.


Mental Force combined with your 3 quintessences will help you get started with 20+ ap every match which will come in handy on every lane no matter who you're facing. Extra damage is never to be neglected or underestimated no matter how small.


Spellsword may be useless for some AP champions such as Blitzcrank (unless you're focusing on dealing damage) but for any AP Carry is a great asset. On Akali, this mastery acts as a lesser copy of her passive which sort of enhance it by adding 5% of your magic damage into your basic damage with every hit.


Archmage has the same effect as Rabadon's Deathcap only less effect (5% instead of 25% increased ability power). Combined with Rabadon, 30% increased ability power will come in handy no matter what.


Executioner is more or less useful. This skill could come in handy when you're chasing someone and want to deal more damage quickly.





This would be the most vital masteries in our build. Now to get on to less vital yet important masteries. Defense and Utility.


Durability will come in really handy especially when you begin a match. You want to buy Boots of Speed so receiving +6 Health per level (+108 Health at champion level 18) will come in handy no matter what others might think. Do not underestimate this mastery. It may offer you the health you need to escape at limit from a fight.


Perseverance allows you not to be kicked quickly out of combat. It's annoying when you need to recall due to low health so this will allow you to stay back a little and then jump back into the fight especially if you're low level.


Hardiness at 1/3 mastery points is not so great but you never know. It will at least reduce a bit of the enemy's basic damage on your champion.


Summoner's Insight is one that you don't want to miss spending a point in. The cooldown reduction will come in handy since you will be needing those summoner spells to get kills and perform combos.

To begin with, I will start talking about why you should take Boots of Speed first and the potions.
You want to be fleet of foot and escape or enter combat fast when you're low level. The masteries and runes will take care of the ability power you receive when you start a match. From here on, you proceed with the builds. I will explain how to build each item and in which order to be very effective.


You want to begin by buying the Blasting Wand, Amplifying Tome and Giant's Belt before making Mercury's Treads. Mercury's will give you more magic defense against AP champions. If you feel they're useless, you can always replace them with Ninja Tabi which will give you armor instead of magic defense.


Rylai's Crystal Scepter is the next item you should create. The health will allow you to fight longer and can prevent you from dying fast in a gank, for example. It's passive is not to be underestimated especially combined with Shroud of Darkness.


Hextech Revolver should be the next item you build right after the scepter. It's spell vamp will be a great asset especially since you're going to use skills a lot.


Liandry's Torment is a good choice because all of it's attributes will come in handy for Akali and I believe they're self-explanatory.


Hextech Gunblade is not to be neglected either. You may want some life-steal and attack damage up since you'll be needing from time to time to go melee on your enemies.


Rabadon's Deathcap is great for it's 120 AP and 25% increased ability power. Great in combination with the Spellsword mastery.


Some might say this is not an ideal item for Akali, but I beg to differ. This is in fact a great item for Akali. Deathfire Grasp is offering a great passive ability during combat [Deals 15% of target champion's maximum Health in Magic Damage then amplifies all magic damage they take by 20% for 4 seconds (60 second cooldown)] and the cooldown will allow you to spam skills more often. You could take Abyssal Scepter but it's really a matter of prefferences since it offers an Aura, it has 30 less AP and instead of cooldown it offers +45 magic resistance. I would suggest the Abyssal Scepter for those that want to play a bit more defensive late-game.

Here is a mid lane result on this build while I was using akali (there were no Kill Steals)

My Team:
Support: Nami
Tank: Singed
Jungler: Warwick (Disconnected)
AD Carry: Graves (Pretty bad played)
AP Carry: Akali

Enemy Team:
Tank: Olaf
AD Carry: Draven
AP Carry: Ryze, Teemo
Tanky/DPS: Kha'Zix