INTRODUCTION
Greetings Summoners! This is my guide for Akali, The Fist of Shadow.She is my main for quite a time now.I have more than 200 victories with her but still think that I'm far away from mastering her.
I want to make something really clear.I'm not saying I'm a pro Akali player I know I'm far from it and I'll never claim it!I really like to play Akali and kinda found my own way to do it.
So please enjoy reading my guide, I'll appreciate any comment, opinion and help you can give. :)
P.S. Sorry for my English.

THE ULTIMATE ASSASSIN
Akali is one of the best assassins in the game, though she should be played with patience and proper timing. Harsh and bully actions with her will probably end bad. Full control over her and good map awareness are the most important things.

PROS
-Very high burst damage
-Great chasing abilities
-Good farmer
-Good harasser
-Decent jungler

CONS
-Squishy melee
-Cripple if focused
-Hard to manage when enemies use Oracles/Wards/CC for/on her
-Need good control over her all the time
RUNES
With these masteries and runes you start with AD Passive on, and activate her AP passive on lvl 2.Of course you can activate her disciplines in diffrent ways, just be sure to have them activated from the very beginning it is a primary thing to do. I start with Amplifying Tome and Health Potion, so i get both passives on 1st lvl. You can feel free to experiment with Greater Mark of Attack Damage and Brute Force (+3 dmg from Offense Mastery Tree.
MASTERIES
21 points on Offense is the way as it should be.Have to admit, I used to play with Defensive masteries.After my skill with Akali raised and I achieved better control over her, I realized that 21 on Offensive is actually the way I should go.It gives her huge boost in damage output.After all, she is an assassin with high burst damage so there is no need to say more. Regardless, if keeping her alive gives you troubles and if you still cannot control her properly then probably is better to play with Defense as a primary tree, or you can use 14/16 to achieve 48 hp from Veteran's Scars talent.
ITEMS
Start with Amplifying Tome and a Health Potion, next investment should be Hextech Revolver and Sorcerer's Shoes.Now you have descent Damage and MP boost, but main thing here is the Spell Vamp you get, thats right - the Spell Vamp. Believe it or not, SV is second to importance after AP. MP comes on 3rd place.Next items to buy should be Sheen and Needlessly Large Rod.If your opponents have more DPS champs than your team do or have heavy nukers you might consider buying Giant's Belt a bit earlier.From this point is important to build up your Rabadon's Deathcap.Here you can make a bit of a change depending how the game is going - from the Sheen you already have, you can build up Trinity Force.AP Akali with those 2 hybrid items: Trinity Force and Hextech Gunblade is one hell of beast out there.When my game goes well I often build Trinity Force myself(with Trinity Force there is a slight change to your items build though).I actually build Rabadon's Deathcap before Rylai's Crystal Scepter.The sooner you get this AP boost, the better.Of course that depends on the game.My last item is a bit optional, with those items it's possible that you don't have the time to buy 6th item because the game can be finished.There is few items you can choose as a 6th depending on the situation - Void Staff, Abyssal Mask, Banshee's Veil, and etc.
The core items I build in every game I play are: Sorcerer's Shoes , Rabadon's Deathcap and Hextech Gunblade.
There are many ways to play Akali because of her possibility to be Hybrid.I'll not start to argue which one is better.I have tried her in many ways myself and with my play style this way suits me most.She must have at least one hybrid item, the best for her are Hextech Gunblade and Trinity Force.
SKILLS
Mark of the Assassin max this skill 1st. Great damage when activated with auto attack and great harassment tool.Double Mark of the Assassin. It's simple enough, you use your Q on the target, wait 2,3 secs until your Q is nearly recharged (your Q is still active on the target at this time), then use R, activate the 1st Q with auto attack, then put on the next Q on the target and activate again. It is really fast process dealing tons of damage.
Twilight Shroud is 1 point wonder, I max this last. It gives you MR and Armor when you are inside.When the time for your W come try to use it around objects, bushes, trees, some wall edges and etc.It'll gives you more possibilities.Don't be harsh to get out from the Shroud.You have 8 secs which is enough time to think your escape path and to deceive your opponents.Sometimes the opportunity present itself.AoE spells and abilities will damage you in the shroud.
Crescent Slash hit all units around you in close range. Staking with AD. Good farming tool.Good ability for a team fights and battles with more than one surrounding enemy.You can use it in combo - Q->R->auto attack->E. You can use it in the "Stinger" way - R->E->Q or Ignite->W->get back, if you want just to hit fast the target and get away, usable when soloing mid.
Shadow Dance at 6th. 11th. 16th lvl - no need any words here, one of the best Ultimates in the game.Doing wonders with Q and E. You can use for escape mechanism as well if there enemies and minions around.Normal combos when chasing should be - Q->R->auto attack->E and repeat, or Q->R->auto attack->Q->auto attack->E->W and etc., of course it depends on the situation and on the hp points of the enemy champ.
SUMMONER SPELLS
I use Flash and Ignite. Flash is great escaping tool. In combination with Twilight Shroud it can makes your escape a lot easier. Flash is good for tower diving as well.You can use it to attack too if you run out of charges on Shadow Dance (this shouldn't happen though).
Ignite is pure dmg finishing spell. You can use it to prevent healing on enemy champ like Mundo's ultimate for example.
SOLO
Akali is surprisingly good when soloing, even against 2 enemies on lane.It is important to keep your HP points safe.When playing against 2 the action is around your tower.You have to be awary of the enemy champs abilities, and you should try to understand sooner the play style of your enemy/ies.Play smart, use short burst hits around your tower, lure them to chase you under the tower, if there are 2, they'll try to take you out for sure.If you are on mid, use 2 wards for the bushes up and down to prevent a gank.If you chase an enemy, be sure to let a few enemy minions behind you to use your R on them to get back faster if necessary. Be more careful against Champs with CC (Veigar,Morgana,Lux etc). The major advantage here is that they use mana and you do not.Lure them to cast their spells, be awary of their cooldowns, harass them and when the time is proper strike for a kill.
TEAM WORK
Akali is good laner with almost any other champ.It is better though, if your partner have CC abilities.Akali really shines with champs like Sion, Malokai, Pantheon, Morgana, Lux and etc.Use your shroud to activate your Q on the enemy wherever you can.Your W is great intimidating and zoning tool.And again, luring the enemy, make them use their abilities and burn their mana pools is important thing to do.
TIPS
As a squishy assassin dealing tons of damage, you should step in to the team fights with care.Don't even think to open a team fight or jump in with the tank.Akali shines when the enemies are at low/mid health.Wait for your team to initiate the fight, your primary targets sre the squishy champs - range AD, casters and etc.
Delay your jump in to action to use Akali full potential.Use the situation to your advantage, be aware when enemies use their abilities in the team fights and when they throw their CC's, ultimates and etc., this is the time to tear them apart.
Akali shines when you have in your team champs like Amumu, Nunu, Malphite, Galio and etc. for their ultimates.
Is a common mistake to chase a kill and give your own life for it.Don't do it.There are a situations that this might be positive (like killing someone on a killing spree to take a good amount of gold), but still - don't do it. Better be Akali with kills/deaths ratio 4/0/3 than 8/7/3.
Akali is a champ who can carry the team in late game(if the game goes well for you of course).So staying alive is a must for her.In the beginning of the game it is vital for you to stay alive.Just don't get killed.You shouldn't go back to base often either.Normally when I begin with my starting items, next time when a go back to base I have 2000-2500g +.Better be that way, than head back to the base every time you have the gold to buy something small, loosing more gold and more exp.
If there is a chance to make a gank on a different lane, go for it, at least you'll help your team mates to push the lane.
Ward your part of the jungle, putting wards all the time can often win the game.The others should do it too.
Go for a red buff when you can it comes in handy for the fights.
When you don't know where the enemies are, be careful walking in the bushes.Better don't go alone or use your W to enter(again, warding is a must).
If you meet an enemy in the bushes and you cannot make a short deal of him, better don't chase him.
If Teemo, Evelyn, Shaco, Twitch and even Akali is one of your enemies - buy an Oracle!If the other team has oracle(s), don't go alone.Don't initiate a fight 1vs1 if you are not aware where your opponents are.Stay with the team and ask them to help you take out the oracle's bearer(s).In team fights you should delay your jump in even further.Make short term bursts and head back.
Don't loose yourself in jungling and minions killing, your team needs you!
Don't use your W in the beginning of the combat, it use huge portion of your energy pool.Use it only when is necessary.You can use it to intimidate or to slow enemies as well.
Before jump on somebody's head I often calculate my dmg according to his health.It's good thing to control the burst and the dmg itself, it's make the fight a lot easier.This way you can avoid throwing away that precious energy of yours.Don't jump like Bull wasting all of your abilities, it will cripple you great if you have to escape fast or if you have to chase further.
When you enter the fight have a clue how can you escape from it if necessary, a safe plan in mind never hurts.With wards you can make this even easier using R on the forest minions.
Akali is not as weak as the ppl think when she is at low health, her high burst dmg can even the odds even against opponent with more hp.Head for the bushes or let him chase, use the environment to help you lure him a bit, then strike fast, the result will talk for itself.This way you can make kills at your tower, just because the ppl are greedy.With one or two shots from the tower you can tear apart stronger opponent pretty easy.
Akali's main advantage is her burst damage, do not forget, and do not loose that.The only way to use it right is if you play AP mainly.(as i said before, at least one Hybrid item is a must)
Don't be greedy - not for a minions, not for a kills.How many games we lost because one of our mates was killing monsters somewhere or was taking the red/blue buff in the same time we were being rape a few yards of him!Never do this, your team needs you as you need them.This is a team game and we should play it this way.
I'll make a few updates for this guide in the future.I'll appreciate any thoughts, comments and hints you can give.
P.S. Apologize for my English again ;)
About Guinsoo's Rageblade (Phever's replay). Guinsoo's Rageblade could be in some help for certain Akali builds.I think for AD/Hybrid Akali build or so.But let's discuss a bit further:First of all GR is an item which reveal it's full potential after few secs(we need to stack it's speed and AP bonus).Now, Akali is a champion who need items that are at full potential at the start of the fight.She is not a champ that will stand there to deal simple hits against her opponents.This is the work for the melee champs like Tryndamere, Olaf, Jax or so.I can aprove GR on some AD/AS build which is not the way I recommend playing her at all(at least my build is far from it).GR is typical, even core Jax's item for example.I don't deny that GR can work for Akali at all, just doesn't work for this build.