Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
This build is highly reliant on your ability to escape situations utilizing both Twilight Shroud and Flash, as it has very little survivability added in the items. I've used this build to great effect in both 5v5 and 3v3 during countless matches. It is VERY squishy though, so make sure that you always have an escape route available. I prefer to engage 1v1, but will enter a team fight after it has already been initiated. Akali can be a solid initiator, but unfortunately you won't have enough health or magic resistance to last more than a second with this item build.
First things first, buy a Doran's Blade and a Health Potion. I realize that the Doran's Blade isn't the most spectacular choice for damage, but it affords you a small amount of survivability while opening up the Attack Damage portion of Akali's passive. The spell vamp passive is a great way to maintain lane presence during early levels, and allows you to build up some nice gold for your first trip back.
Starting off in lane, as always, your primary harassment is going to come from Mark of the Assassin. It's a solid skill, and allows for decent champion damage as well as excellent last hit potential. You need one rank of both Twilight Shroud and Crescent Slash to enable you to escape and kill creep waves. Other than that, just stay in lane and do your thing until you get around 1,000g or level 6, whichever comes first. They should typically come around the same time if you've been getting in plenty of last hits and maybe a champion kill or two.
Go back and purchase either a Giant's Belt or an Amplifying Tome and Boots of Speed, depending on how the game's going. If you've been doing well, it might be a good time to consider investing in a Mejai's Soulstealer. I don't typically go this route, as it's somewhat of a risk, but it's a decent option.
From anywhere from six to eight, you should be considering running amok through the jungle, and popping out for ganks. Make sure to coordinate with your team for them to initiate or set up a gank, and get ready. I generally will try to get a Mark of the Assassin for using Shadow Dance, as it gives you that initial burst that Akali is so well known for. Follow immediately with a Crescent Slash, and you should have a decent chunk of their health gone. If you're not in any danger of being ganked, just rinse and repeat until the enemy is dead. :D
At some point, you're going to have to go back, and I highly recommend finishing your Rylai's before you get anything else. It adds the utility Akali needs to chase and gives your teammates a chance to catch up as well. From here on out, just follow the same basic principles, and try not to die. If you die more than twice before the laning phase is over, you may want to consider a change of tactics.
More will come as needed.