Akali is burst damage and very squishy... you have to go in the and out of the battel, like harassing.

At the beginning of the game Doran's Blade or with Amplifying tome(if you want to rush sheen) after you get the sheen, get a boot, then get some spell vamp(Hextech Revolver) finish the Will of the Ancients. By this time if you already owning the other team finish the Lich Bane and if you balance in kills get the Rylai's Crystal Scepter, to give you the extra health to do more damage ;) and then Lich Bane. After that is should be end game already. The Rest is all up to you and the situation of the battle. If the other team have a lot of Magic Resist go for the Void Staff. if not Deathcap :)

Before level six you just want to play passive. Once level six wait till you have three charges in you're shadow kick before going in. You initiate with your "Q"(wait a second)then "R","Q","W"."R","E","Q","R","E". and if the champion isnt dead by then, harass with Q and R. During Team Battle. They are going to focus you because you do a lot a damage in such a low amount of time. When your team initiate wait around in the back till you see one of the enemy with 75% of health and then and only then go in, unless its a clear advantage.