This is a build I have used time and time again in solo queue, and it always works nigh flawlessly. Of course it doesn't make you invincible, and it doesn't apply to all situations. However, it brings out the power Akali has.

The runes took a lot of time, thought, and testing to perfect. As I said, they don't apply to everything, but they are very versatile.

I like to go 21/0/9, taking normal AP in offense and mobility in utility. I like to go for summoner spell cooldowns so that you have that flash up more quickly to do flash/ult for extra chasing ability that is up more often. Also, lifesteal and spell vamp synergize incredibly well with her passive.

Doran's shield regeneration is incredibly powerful early on and will keep you regenerating quickly, and possibly keeping you in lane throughout the laning phase.

If there is one thing that I emphasize about this items, DO NOT TAKE GUNBLADE FIRST. It is one of the least cost-effective items early in the game for a champion like Akali. Instead, take Rylai's, since it provides much-needed durability and decent CC, since hers is atrocious, being only the AoE slow on her stealth, which she needs for other things. After getting Rylai's, gun blade is valid. Once she has some durability, the sustain it gives is invaluable and can give you the ability to fight on low health very effectively.

This I say because of Akali's "all-in" playstyle. This requires durability so you can be in the middle of the enemy group but still alive and insta-gibbed.

This varies based on the player. If you want high damage output early, but more difficult farming, max E first. It deals physical damage and scales better with AD, and most players won't know how to build against it since AP is the norm on Akali. However, it is melee, leaving you helpless with it unless you can just walk up to them before level 6, or it leaves you in requirement of a stack on your R. If you are against a ranged opponent, or even just want to play safe, max Q first. It has greater damage late game when you proc the mark, scales with AP, has a relatively low cooldown, and has a decent range. Last hitting creeps will be very taxing in energy, since it has a high cost. However, it puts you in less danger, so if you're willing to farm slowly, kill quickly, and miss some creeps, this is the skill you should max.

Pros
-Extreme burst
-Stealth
-Doesn't run on mana
-Spell vamp
-Deals bonus damage on auto attacks
-High mobility
-Ult stack on kill
-Snowballs hard

Cons
-Inherently squishy
-Melee
-Stacks on ultimate, long time to replenish
-Weak before 6
-Short range

Akali cannot solo. Even with incredible sustain, burst is incredibly powerful and essentially the only counter play mechanic that works against her. She NEEDS teammates to apply extra sustained damage and defense.

Akali is melee, making her disadvantageous in mid. With her Q, she can farm, and when starting, you should Q-auto the first melee minion. This provides a little extra advantage in lane if you can push, or a little bit of time before being pushed under tower if you're zoned. If you have lane dominance, farming is safe and easy. If not, you have to snipe minions with Q.