Hey MOBAFire,
I was thinking one day about making a guide and, well, I did! This is my first guide so I might leave out a few important things. If I do just notify me. Anyways, this is my Akali build. This is how I like to play Akali and it isn't very far off from other Akali players. Though I do have a few tweaks to mine (mainly boots of mobility and rushing Rylai's) but I'll get into that later. Akali is a melee attacker whose skills scale off of AP. Akali is a very unique champion with a unique playstyle to follow suit.

Pros:
VERY great burst mid/late game.
Versitile on how you can build her
8 second confined stealth with Twilight Shroud
Easy escape with Twilight Shroud and Shadow Dance
Racks up kills easily

Cons:
Squishy as all hell.
CC-less (besides Rylai's and the slow from Twilight Shroud)
No AoE
Takes some time to get used to, especially in team fights

Q-Mark Of The Assassin
You throw your gardening tool-thing at the enemy and it puts a mark on them. If you hit them when they have the mark it does bonus magic damage. Great skill for mid/late game damage. Also excellent for farming. Early game the damage kinda sucks and it is risky to try it on an enemy champion.
W- Twilight Shroud
You throw down a circle and as long as you are in the circle you are stealthed and gain bonus armor and magic resist. If you attack you are revealed to the enemy team for a brief duration. The circle lasts for 8 seconds and will slow any enemy unit that passes through. This a great skill for getting out of sticky situations or getting yourself into someone else's sticky situation. Good for checking bushes safely and slowing the running enemy champion
E-Crescent Slash
You do damage to nearby enemy units based on AD and AP. Eh... This skill is okay. I use it just do do that little extra damage when my Q is on cooldown. It's good for farming, but not nearly as good as Mark of The Assassin.
R-Shadow Dance
Level 6 GG. You dash to target enemy. That's it. Why is it so good? Well it is limited by Essence Of Shadow. You gain one every kill or assist you get, or every few seconds. The way you use this in conjunction with your other skills is what makes or breaks you.

When going 1v1 against someone, you will most likely use this combo:
W-Q-R-AA-E-Q-AA-R-E-W-Q-AA-R-E

By that time they are either dead, or you realize they have way too much MR to go 1v1. The first W is to initiate, place it so that the are on the opposite edge of their main escape route so they either have to walk all the way through it or come towards you. Throw your Q and back off. You heard me, back off. Just for a split second or two, to give the enemy some confidence. Then rush back in with your R, get the bonus Magic Damage from MoA and your Auto Attack, then use your E as that extra little damage. Rinse, and repeat, remembering to pop your W when you can. Remember to play a little passively. Just poke at them a little before, unless you know you can kill them with a full combo. Don't be afraid to use your skills; that is the glorious thing about energy!

I go for 2 Magic Pen Marks and the rest AD. The reason is to trigger the passive, Twin Disciplines. Armor Seals for extra sustainability because she is so squishy. AP glyphs and Quints again, to trigger the passive.

21/0/9 for everything AP in the offense tree and everything non mana related in Utility. You could go 21/9/0 if you want, it is just personal preference.

Why rush Rylai's?
Because Rylai's is such a good item on Akali. The Slow, AP, and Health? Dang! The enemy team better get tenacity or stack MR. It makes chasing people easy and team fights even easier.

Why Boots of Mobility?
I know I'm going to get a lot of Flak for this. I just know it. You can get Sorcerer Shoes or Merc Treads and they would be good, but I like the Boots of Mobility a lot better. It enables her to get into the action a lot faster. Since you are primarily a 1v1 champion, you will most likely be a split pusher on top or bottom while your team holds out mid. But once things get a little out of hand, it is nice to be able to get there in around 20 seconds. And trust me, an Akali in a team fight can make the hugest difference.

The rest is pretty straight-forward.
Lich bane for the Procs, Gunblade for the AP and AD AND it's active (Never underestimate gunblade's active), Deathcap for the insane AP and Banshee's veil for those annoying little mages (IS THAT A SHORT JOKE?-Veigar) This build works wonders with the playstyle I mentioned.

The skill sequence should be like this:
Top Priority: Shadow Dance
2nd: Mark of the Assassin
3rd: Crescent Slash
4th: Twilight Shroud

I take Flash and Ignite for 2 reasons. One ignite is good on anyone, it gives that little extra damage to kill people. Two, flash is good on anyone, but very good on Akali, or anyone who can stealth for that matter. Just pop your W when things get out of hand and Flash out. It is also really fun to juke the wits out of people!

Well first guide, I think I did okay, but that's just me being easy on myself. Let me know how I did and how I can improve on guide-making. Akali is a great champion and can dish out tons of damage with this build. Oh and she has big boobs but that's another story.