As Akali "The Ninja Nuke" the idea is to build equal AP and AD to keep both her twin disciplines fully used. Getting boots that are geared towards what team you are against, makes her more durable, however she should be more of a "Get in, do some damage, Run!!" Flash and Ghost support both chasing and escaping. The slows and massive sudden damage from Tri Force and Rylai's will not let anyone escape her.

In the Laning phase just last hit with Mark Of The Assassin, and Crescent Slash when you know you will get a lot of minion gold. I have found that without a lot of gold and experience at the start of the game, Akali doesnt perform as well later on as she cannot dish out as much damage.

Key Points

Twilight shroud near a wall, then flash is a great escape mechanism.

NEVER get snowball items unless you get 2 Champion Kills before going back to base first time, after the laning phase has begun.

Even on low health keep attacking, as the spell vamp and lifesteal will keep you alive, many a time i have survived on just <100 health

Spells

Flash allows access through walls, into your twilight shroud (to drop behind enemy), to escape, to allow you to land your Shadow Dance.
Ghost allows you to chase or run faster, can be replaced with either

igniteor exhaust, if you feel more aggresive.

Teleportis useful, but only in 5vs5.

Runes

(Not too sure about how to explain runes at present point in time)

Is a great starting item, where you get Health, Damage and Lifesteal (All things Akali needs)
Obvious really, you want to go places faster.
Get Merc Treads for CC and AP heavy teams.
Ninja Tabi are more useful however, and provide Armour, thus get these for AD or Burst Heavy teams.
Rylai's Crystal Scepter allows for slows on your abilites, compounding on the fact you should be using your abilites for slows, and spell vamp.
Rageblade is great for constant attacking, and gives you more reason to keep attacking, for spell vamp and increased damage and MD.
Great for adding extra burst damage when you use MOTA or Shadow Dance, and starts your Tri Force.
Tri Force allows for greater burst damage on you auto attacks, after hitting the enemy with Shadow Dance.
Hextech gives everything Akali wants, AP and AD, and a decent extra nuke shot. Most people rush thi first but i find building her up slightly tanky boasts better in the long run.
Deathcap will allow your AP to maximise your AP, building on your Twin Disciplines.

Ninja Style

In, damage, out. Simples

She is a Nuke she finishes, never initates, unless you are a few levels higher or have a snowball item.