Hi this is my first guide ever so excuse me if the layout of the build is not top notch.
I have been playing akali for a few weeks now and I find her to be an excellent champion at picking down pretty much anything in your path. Especially if you get mid. Let me explain why:

You would want to go mid lane for numerous reasons. First, the enemy cant stop you when you reach lvl 6 with the proper items. But be wary, the first 6 lvls and up to the point you get a hextech revolver will be pretty much just you standing back and farming with your Q. Use your W to farm those minions in the back without getting harrassed. At lvl 6 you would want to go back to the base (asuming you got the gold for a hextech). If you do, then proceed jumping on your enemy and shred his ******* inside out. I dont feel that this part needs that much of explaining. Just use your head. Then proceed doing this for the rest of the game.

http://img291.imageshack.us/i/akalimatchhistory.png/

My runes are the following:
Magic penetration marks
Flat Armor seals (dodge works just as good if not better)
Ability power/lvl glyph
Magic penetration quints

The red runes is an obvious choice, do not need to be explained.

I tend to go with the armor seals because if you are going mid (in which you will be doing in this build) you have be resistant to fellows with constant damage output such as corki or ashe. This is because the incredibly defense type of gaming you will have to endure the first 6 lvls and 730 gold into the game.

The glyphs: Here you will definitly want to go with the ability power/lvl glyphs because the game REALLY starts for the mid-akali 6 lvls in. At this point the stacking AP runes will give you a much greater bonus ability-wise than the flat would do. TL;DR? Just go with stacking.

Quints: Obvious reason is obvious.

I go with 9/21/0 taking down to 15% spell penetration in offense then maxing the defense tree going magic resist, armor, dodge, nimbleness, harden skin, veterans scar, ardor and tenacity.

Amplifying tome - Health Potion - Hextech Revolver - Boots - Hextech Gunblade - Boots of Swiftness or Mercury threads

These are the first items you would want. Maybe throw in a mejai and sword of the occult in there if its going good (and it will if you obey the guide). Also get a rylai and guardian angel. Guardian angel will help you keep your stacks of mejai and occult. If you feel that your team has alot of CC you could actually skip the rylai and go for the rabadons.

Also bear in mind the enemy teams settup and adjust accordingly.

In teamfights you want someone else to engage and when you see the enemy team dropping some cd:s on your team, you jump in at the people in the back and kill the as fast as possible.

If you end up surrounded in your shroud there is a few things you can do if you dont have a way to escape. If one of the people surrounding you have a great escape ability such as "kassadin" or "ezreal", jump him. make him flee from his team and use you ultimate to keep up with him. If succesfull he will flee from his team, thus saving you by giving you some distance between you and the enemy team and giving you a kill (most likely).

Pros: Extremely lane dominant at lvl 6
High burst
Extremely good chaser
Easy to KS
Decent escape

Cons: Some difficulty to master
Weak early game
Squishy

Go with ignite and flash. Flash so you can confuse them when flashing behind a wall while in your shroud.

Ignite to get those kills that would have survived your tower dive.

Use your Q to farm early, then you should be focusing on kills and not that much of farm. Keep yourself at a normal creep score.