Akali can be played different ways, but the real way to play her is going nearly all AP. By lvl 18 if you have just 4 Items build (Say your having an average game) you will have "+136% Additional Magic Damage" & "Akali's Abilities heal her for 30% of damage dealt". This is not including the additional +20% Life Steal and +20% Spell Vamp from your Hextech Gunblade. At full build it comes out to "+168% Additional Magic Damage" & "30%-38% Healed from Abilities"
With this setup your Killing your enemies in 3-6 attacks {Not Tanks} and with continual non-stop burst lasting an entire team fight. So while dealing Crushing damage your Gaining more health back than an AD Akali would be. She also will be doing continual non-stop burstings throughout an entire team fight.

You can see this build play out here! http://www.youtube.com/watch?v=4oAeHjhSqRE

The site does not carry Energy Regen Runes so i left them blank and will Show them here! Because of this i added 9 Quints of watever instead of the optional 2 to fill up Rune slots that had to be filled.

Marks: 8x{+96 Attack Damage}, 1x{+.95 Magic Pen}
Seals: 9x{+.64 Energy Regen per 5}
Glyphs: 5x{-.65% Cooldowns}, 4x{.57 Magic Pen}
Quints: 2x{+2% Experience Gain}, 1x{+2.25 Attack Damage}

The +10 Attack Damage at start will proc the Life Steal buff allowing you easy access to both Buffs at start for Maximum Damage and Lane Time. -5% Cooldowns for Constant burst Lasting an entire team fight. +3 Magic Pen to Counter champs like Ramas or Galio early game.

Ignite for that finishing First blood kill {Trust me it helps a lot} and Flash for good Escape and Attack tactics. Another good choice would be Exhaust, as Akali's dash can take the place of ignite.

One of my favorite aspects of Akali is her Bubble Tricks, think you can juke out an enemy at any turn? Want to do it invisible? Placing her bubble on the outskirts of a bush can let you scout a bush {Use-full at start} or if your being chased down a lane you can pop it mid lane, while next to a bush {Remember when you leave the bubble you get about half a second before you appear} and run right into it while your pursuars chase ahead. Just recall bak, or if the come back for you, dash out at the farthest one, Double Juke? Use her bubble to unlock some of the most Unique of escapes and attack tactics. Enemies will often forget about her dash and if you decide to bubble while there farmming, simply walk to the edge, dash out, 1 down, run bak in, *INVIS*, dash out, DOUBLE KILL!!!

With this build Akali can effectively 1v1 most champs, or even 1v2. {Not Tanks} If a Twisted Fate tele's to you when you are at quarter hp, feel free to 360 and end his world and walk out full hp. Like i said Devastating damage that then turns to Life Steal. Although while in a team fight, she tends to be one of the first to be focused on account of her moderate HP and her need for close hand combat. To counter this, simply use your Twilight Shroud. While it wont keep you safe from AOE's(though does increase resistance and slow) you cannot be targeted {Inless they buy an oracles} and can simply circle around your enimies for your quik burst {Dash-bubble(if not up already)-Spin thing-Karma-Auto Attack. Dissapear for half a second only to re-emerge on another enemy or finish of your prey.
ALSO!!!
TRUST YOUR TANK! If you know you have a good tank, FOLLOW HIM INTO BATTLE! since you are so up close your quik dashes are suprising and with a good tank your 2 could triple kill with ease.
LASTLY!!!
SAVE YOUR TEAM!!! Ashe being chased down a lane by Mord and Sion? Dash in, Bubble, and Flash/dash/run out, simply doing so will turn there attention away to you, but wait, they cant see u, now your both gone. If they stayed on Ashe or whoever, well then you just killed them.

After lvl 6 as long as u dont put anything in Ur bubble till last {other than first level} it really matters on weather your heavy farming or heavy harassing. If the enemy if preventing a farm, improve your Kama and use it to last hit and harass, if your farming, improve your Spin for much more minion damage out put and better life steal.

Red Buff is your best friend. You can first easily acquire it at lvl 8-9 without potions, and can solo Dragon at 12.

Pros:
Akali is great at adapting to any champion and using different techniques to counter them and heavy harass. No matter the situation she always has a way to overcome it {See Skill Sequence} and using it to her advantage. Can literally 3 shot Ashe (quick burst) and Dominates all Squishies and most Casters.

Cons:
The only real Con is that if you get under leveled early or Start to fall behind, its hard to recover. If you do not know Akali's limits and know how to use her abilities to there potential, it may be a challenge to adapt to a Quickly changed environment (I Suggest a custom game or 2.. er 3)

Obviously your item build will be different depending on what your up against, but the big idea is to build up as much ability power as you can, while keeping the hextech for its extreme effectiveness. If your having a hard time farming because your low health at start is just not doing it for a tank or something, skip the mejas and go right for it, if your doing good but can get in too many kills, go for your rabadons be4 hand. Simply changing your first 2 build items becomes handy in many situations.

One of my favorite aspects of Akali is her Bubble Tricks, think you can juke out an enemy at any turn? Want to do it invisible? Placing her bubble on the outskirts of a bush can let you scout a bush {Use-full at start} or if your being chased down a lane you can pop it mid lane, while next to a bush {Remember when you leave the bubble you get about half a second before you appear} and run right into it while your pursuars chase ahead. Just recall bak, or if the come back for you, dash out at the farthest one, Double Juke? Use her bubble to unlock some of the most Unique of escapes and attack tactics. Enemies will often forget about her dash and if you decide to bubble while there farmming, simply walk to the edge, dash out, 1 down, run bak in, *INVIS*, dash out, DOUBLE KILL!!!