This build of Akali has done me very well in the past two dozen games or so, with a few variations. The main idea behind the build is to ramp up attack speed and ability power, with a minor increase in health. Mind you, this is my current build, and the runes/masteries are going to all end up tier 3 eventually.

So, early game, getting longsword helps, because you gain spell vamp, which means that you shouldn't have to buy potions, since your abilities will now heal you. The next thing to go for is berserker's greaves, for both the attack speed boost and the addition of movement 2. While working on rageblade, I suggest either selling the longsword to afford the pickaxe or the rageblade itself (this can be finished by lvl 9-10). Do not sell the longsword to get the blasting wand, as you want both to have both disciplines at once. After buying the rageblade, you can choose to either go for deathcap or lich bane. It shouldn't matter what order you get them in, though deathcap is cheaper, so you should be able to get it sooner. By the time you have both lich bane and deathcap, the game will be at least 30 minutes long, and there will be a team in the lead.Rylai's is mostly for the health and the slow, but the extra AP doesn't hurt. If the game still isn't done, build either Force of Nature, or something that blocks physical damage, depending on what the enemy team has for players.

Heal and Ghost.

Heal:
Akali is sort of squishy, so heal is always useful on her.

Ghost:
This is used either to run when hurt, run while evading people(hiding in shroud then running away), or for getting to a fight.

This version of Akali is great(in my experience) at taking down the mages and DPS players during team fights, allowing for quicker team battles and easier times ganking tanks. By lvl 11 or 12, you should be able to take on dragon alone, or take either blue or red buff, depending on what you choose to do.

In the negative, my style of playing Akali usually results in my death after getting 1, maybe 2 kills, simply because she is a squishy character who is meant to end things, not initiate. As long as you play her safely, you should be able to end up with a 1:1 kill/death ratio.