Doran's Blade is the best starting item you can get for akali. You need the 10 AD for you passive to gain Spell Vamp. Furthermore it gives some HP and Lifesteal which makes it much more valuable than Long Sword.

When you first go back get Boots and Sheen if you have the money for it. But Boots is needed to get back to your lane fast.

On your second return get a Hextech Revolver for a bit more Spell Vamp. and some extra AP. Also try to get Mercury's Treads for Tenacity and the Magic Resistance which you will need a lot.

Now in the Mid Game getting Rylai's Crystal Scepter grants you a nice HP boost, AP and some slow. For getting this start with the Blasting Wand and then go for the Giant's Belt.

Getting Rabadon's Deathcap now is the best situation to boost your AP.
With the bonus AP by Rabadon's Deathcap the upgrade of Sheen to Lichbane is pretty nice because now you have 3 times the AP than AD.

Your damage output is pretty nice now so get the upgrad to Hextech Gunblade for nice heal and some nice slow.

Well the basic item sequence is done now. Now watch out if your enemies are Hard AD or Hard AP. If they are very focused on AD get the Guardian Angel and sell the Doran's Blade. If they are hard AP get Abyssal Mask and sell the Doran's Blade. If it is a balanced team also get Abyssal Mask because only nukes can really kill you.

Btw. the Health Potion in the item sequence are just for some space between the items to show you what is the basic sequence and what not ;)

So.. i wish you gl and hf now :) and I hope it helped you a bit^^

Just a Reflex