This is my first guide and I didn't read over it before I published it. So please, if there are any mistakes, grammar or spelling wise, please tell me in the comments below.

Akali is an amazing early game harasser. She is an amazing chaser and escapist, being able to fake out enemy champions with your Twilight Shroud. When deciding on if you should play Akali or not in a Draft game, you have to consider the enemy team. Champions that are tanky with CC can counter her well if not prepared.

When playing as Akali, people can get very annoyed of you. She can dash into a fight and easily steal a kill from someone because of the insane amount of burst damage that she can put out in a such a short time.

When playing as Akali, never build her AD. Her maximum potential comes out when she is built AP. The only AD item you should get on her is the Hextech Gunblade for the Spell Vamp and the AD to activate your passive ability.

The only thing that makes Akali cry is an Oracle. When the enemy team has one, you can't face check the bushes as well with your TS and it'll make escaping in the middle of a battle harder.

Mark of the Assassin - MotA
Twilight Shroud - TS
Crescent Slash - CS
Shadow Dance - SD

Attack Damage - AD
Ability Power - AP
Magic Resist - MR

Pros:
-Fun to play
-Amazing assassin
-Great at farming and laning
-Can jungle decently
-Insane burst damage
-Great at chasing/ganking/juking
-Super Anti-carry

Cons:
-Squishy
-Countered by Oracle's/getting focused/and CC
-Needs skill to play
-Have to be aware/make good decisions

Akali NEEDS her passives to be activated and strong. It makes her much stronger, able to deal out more burst damage, and let's her survive longer. It let's her have more spell vamp and bonus magic damage. You have to have a minimum of 20 AP for Discipline of Force (red on left hand) and 10 AD for Discipline of Might (green on right hand).

Usually I would buy the runes that scale as you level up, but those won't give you enough AP or AD to have both passives at the beginning of the game. Because you have a decent about of AP early game, you can punish anyone that tries to over extend themselves to attack you. Once you hit level 2, you should be harassing the enemy champions with your TS, and your MotA.

I go 21/0/9 is the best way to go. 21 in offense because it helps get through enemy armor, last hit minions better, and the increase in your damage will help out significantly. You shouldn't need any points in defense because your twilight shroud hides you and give you bonus armor and magic resistance, plus slowing down enemies. 9 points in Utility helps with staying in lane longer.

Why?
This will let you chase easier, escape dangerous ganks, juke enemies, and steal buffs.

Obvious, use on an enemy if they are about to die and you can't catch up. And with your masteries, you'll get an extra +10 AP on cooldown.

Starting Items

Getting a Doran's Blade at the beginning of the game helps out your AD passive and gives you more spell vamp. I say go over the AD passive over the AP passive because the survivability is more important to stay in the lane longer.

First time going back

+ or
Try to stay in lane until you have at least 1,800 or more gold. This way you will have enough money to buy the Boots and possibly a Hextech Revolver. If not, buy the boots of speed and one or two Amplifying Tome.

Boots of Choice

or
I try to go with the Sorcerer's Shoes to deal more damage. But if you are having troubles with a lot of CC problems, get the Mercury's Treads.

Midgame Items

+ (if you are doing well)
By midgame, you should have the Rylai's Crystal Scepter and possibly another Blasting Wand. If not, then hopefully a Blasting Wand and Giant's Belt. If you are feeling good and you know that you are going to be dominating in that game, then go buy a Mejai's Soulstealer before the Rylai's Crystal Scepter.

Late Game Items

or + or + + +
Situational Items or or or or
By now you should have the Doran's Blade if you haven't sold it yet, either the Sorcerer's Shoes or the Mercury's Treads, the Hextech Revolver, the Rylai's Crystal Scepter, the Rabadon's Deathcap, and hopefully the Lich Bane. I usually finish the Hextech Gunblade lastly or second to last. Those are only 5 final items because the last item depends on how the game is going. You could either have the Mejai's Soulstealer if you are dominating and getting multiple kills, Void Staff if the enemy builds a lot of MR, Guardian Angel for survivability and defense, and Zhonya's Hourglass for survivability in a fight. If you really want the Sorcerer's Shoes and still want tenacity, you could get the Moonflair Spellblade, but I never have.

Core Items

You have to have the Rylai's Crystal Scepter and the Lich Bane. These two items are going to help you out the most for damage and survivability. The Rylai's if amazing for chasing when you throw your MotA at someone and it slows them down. When using the Lich Bane, it is a lot easier to take down turrets, barracks, and the nexus. Just press E and it'll power up your auto attack and it could hit possibly 500 on the structure.

Passive: Twin Disciplines

Upon obtaining 19.5 additional ability power, Akali's hits deal 10% bonus magic damage, increasing by 1% for every 5 ability power gained thereafter.

Upon obtaining 9.5 additional attack damage, Akali gains 10% Spell Vamp, increasing by an additional 1% for every 10 attack damage gained thereafter.

What it is:
This is Akali's passive. I get this immediately at level 1 from my runes and the Doran's Blade. Having both passives early is vital for her best early laning phase, survivability, and damage output.

Q-Mark of the Assassin

Akali spins her kama at a target enemy to deal 50 / 75 / 100 / 125 / 150 (+40% of ability power) magic damage and mark the target for 6 seconds.

Akali's melee attacks against a marked target will trigger and consume the mark to cause 50 / 75 / 100 / 125 / 150 (+40% of ability power) magic damage and restore 20 / 25 / 30 / 35 / 40 energy.

Cost 60 energy
Range 600

What it is:
This is Akali's first and most important skill that she learns. It is the main source of your burst damage output, and what makes her powerful. Using this ability, you will throw your kama at an enemy dealing damage, then attacking the enemy with your auto-attack will deal even more damage to that unit, and replenishing some energy.

W-Twilight Shroud

Akali throws down a cover of smoke that lasts for 8 / 8 / 8 / 8 / 8 seconds. While inside the area, Akali gains 10 / 20 / 30 / 40 / 50 armor and magic resist and becomes stealthed. Attacking or using abilities will briefly reveal her.

Enemies inside the smoke have their movement speed reduced by 14 / 18 / 22 / 26 / 30%.

Cost 80 / 75 / 70 / 65 / 60 energy
Range 700

What it is:
This is Akali's second ability and what makes her the assassin she is. This can be used for anything you need to do. Whether that be killing minions, scaring off enemies, harassing enemies, killing enemy champs, escaping, and reducing damage income.

In your early laning phase when you need to farm and kill those minions but you can't because an enemy champion is by them, throw down your TS. Not only will you be able to sneak into the minions and kill them, but you will most defiantly scare off the enemies that are near you. They think that you are going to attack them, so they back off, giving you time to MotA a minion and kill it without any damage taken.

If you are getting pushed back in your lane too hard, throw down your TS, go cloaked, then harass the enemy if they are near. Remember, you have a whole 8 seconds to do something to them, make good use of it.

Killing enemy champs has the same concept. But what I try to do sometimes is throw my TS on top of an enemy so it slows them, then run at them, or SD to them if you are level 6+, then use your ability combo to unleash your insane burst damage.

Escaping with this skill is fun and rewarding if you do something amazing. If you are in trouble throw it down and fake out the enemies if you can. The best thing I can say is use your TS and try to SD to a enemy/neutral creep that is far away. Or just use flash.

One last use for the TS is to decrease damage income. Let's say Karthus uses his ultimate and you are about dead. Use your Twilight Shroud and stay in it. You'll get that extra Magic Resist and you could live through it.

E-Crescent Slash

Akali flourishes her kamas, hitting nearby units for 30 / 55 / 80 / 105 / 130 physical damage (+30% of ability power) + 60% Attack Damage.

Cost 60 energy
Range 325

What it is:
This is Akali's third ability and is her main source of farming. Using this late game will bring minions down to such low HP to where you can kill them in auto-attack. On a 1v1 fight, you can use this, but it isn't effective as your Q would be.

In a team fight, try to never use this. Takes up too much energy and doesn't give any back. Your Q is the best bet.

R-Shadow Dance

Akali moves through shadows to quickly strike her target, dealing 100 / 175 / 250 (+50% of ability power) magic damage.

Akali stores an Essence of Shadow on kills and assists as well as every 25 / 20 / 15 seconds up to 3 total.

Cost 1 Essence of Shadow
Range 800

What is it:
This is Akali's ultimate and where do I start? This ult is amazingly useful for anything. Stealing dragon, stealing Baron, chasing enemies, dashing to minions to get away from enemies. I've stolen dragon and Baron a number of times from being able to Dash through the walls and take the kill because of how much damage this skill can output. And after stealing the kill, just flash out over the wall.

Don't spam this early game. I can't stress this enough. It's frustrating when you don't have enough Essence of Shadows to chase an enemy or gank them. Try not to gank with only one Essence of Shadow unless the enemy is low. You won't have enough to chase if they ghost or flash away.

Maxing out your Q is the first thing you should do. It is your main damage source and very useful to harass early on with. Put only one point into your Twilight Shroud early on because it is your only way to defend yourself. Max out your E after your Q, then your R and lastly your W.

Best burst damage combo
Q + R + Auto-attack + Q + Auto-attack
The enemy should be dead. If not, just repeat the combo.

Combo to poke with
Q + R + Auto-attack + E

Akali is a great at 1v1s. Use your TS wisely and use your Q as your main source of damage. Only use R to catch up to and enemy or escape if you get ganked.

In a 2v2 fight, let someone else start it if they are more bulkier. If not, then throw down your TS and start the fight. Signal the enemy you are going to go for, and start to melt them down.

In a 5v5 team fight, never be the initiator. You'll die quickly and get focused. You have to stay in the back and pick off their carries/squishies.

Akali can tower dive very well. Her R let's her dash at them from far and get her combo off, then escape using R on a minion or flashing away.

Part 1 Play Video
Part 2 Play Video I can't record the game on my laptop so I posted a game of my friend that recorded it and I was in it playing.