I have tried countless builds on Moba and many many that just randomly came to me.
Out of all of them, one shines, and I wish to thank you HeAt for getting my Akali experience off the ground with your build.

For my runes I use an assortment of sets but will nearly always stick with ad marks , dodge seals , ap per lvl glyphs , and flat ap quints . I did, at one point, use flat ap glyphs but found I like ap per lvl better. I am nearly done with grabbing all the flat energy regens to test. Exciting.

Akali is a pretty squishy character and even though I personally do not play very cautiously I do believe a few points in defense is best for her. So i go with a 14/16/0 build. There have been times where Ive done 21/9/0 (which will probly end up the one I use once I get my energy regens), and even 21/0/9 for jungling. Most of the time stick to the 14/16/0 since it works the best for me and my play style.

As I stated before. This is the way I build, you dont have to like it. I just wanted to share.

Sheen offers a tremendous boost in dmg early game and once you buy a single ap item your ap rises above your ad so please upgrade quickly to a Lich Bane for though-out game maximum dmg.

Here is where you decide on boots. Boots of Swiftness are my normal choice although I do find myself picking Sorcerer's Boots and Boots of Mobility alot. There are alot of guides that suggest Merc treds and I say nay. If you get focused starting with CC and dont have Quicksilver Sash or Cleanse, you are most likely dead and Im sorry.

Then get yourself a hextech revolver > gunblade for that survivability and clicky shot. Followed closely by a Rylai's for that "you can't get away from me feeling" and a little more survivability.

The Rageblade. I have put this in at various different points in all of my builds. Akali just simple is not Akali without it however, I feel that it works the best for me at this stage. A side not about the Rageblade is that Akali murderizes towers and that is all there really is to it. If you feel that this is the most important thing for you and will support your team the most. Please get this item earlier and destroy those towers. Just get it after your Lich Bane for sustained dmg.

And your last item can pretty much be an assortment of things. I find myself nearly always using the Deathcap though. Lots of ap = lots of burst death. Also if you are a real thorn in the opposite teams sides then please by all means get a Guardian Angel for the laughs of resurrection and murder once they "blow their load" so to speak on killing you.

Standard Q > R > melee > Q melee > E normally does the trick for a squishy. Always shoot for that double mark.
I see alot of Akali R > Q > melee also and i feel its in bad form. Do it if you absolutely have to but try to stick with the double mark as often as possible for your extreme burst.

The use of your W is entirely situational and I am not going to tell you how to use it. Play her and learn to use it with your own style. There are plenty of Youtube videos that can give you better ideas than I could explain to you.

If you have to read something by me then use it when you are in danger of dying or need that little bit extra armor and magic resist to kill that . Gl with this skill. I am learning new ways to use it every day.

What to put here.
I have personally struggled with deciding on Akali's masteries. I am going to say use whats comfortable to you.
For this guide I put Flash and Exhaust just because it is what I most often use. The exhaust for that little bit of edge in a fight and the magic resist reduction. Flash more to get you in close and kill. Alot of people flash out of her smoke bomb and run away or over a wall to run away and while that works I would rather use flash more offensively. Mostly early game, pre 6, or maybe some way they started a fight with me and I just didnt have those Ultimate charges.

Back to what i said earlier though use anything that works for you. Ive used exhaust ignite and flash ignite also.

In summary please remember this is just the way I play and I am no pro.
Akali is an anti carry/caster in my opinion and if you have to die for your team to win then so be it.