Hi there, i see you are having a bit of trouble with Akali, well almost every Alkali player has trouble with her in first few games.
In terms of build, always get Hextech Gunblade first as it provides OP sustain and give you a bit of Ability to increase, q and e and ult damage.
I would then buy Crystal Sceptre as it gives Ability and Health to give Alkali that bit more health needed in clutch fights.
I would then get Rabadon's Deathcap as is gives so much Ability and by then you will have carry potential.
Then get Ludens Echo for movement speed, over Lich Bane and then get Zhonyas Hourglass and finally Sorcerers.
At the start of the game, Akali is a mid lane or solo top, well that how its played mostly so you need to ask junglers and top and bot to give frequent ganks and just try to get as much farm as possible and never give early kills. Never fall behind in cs, it will cost you dearly. Over all you need to be really careful pre level 6 an once you hit level six and have Hextech Gunblade, you can start roaming and helping top and bot.
You just need to get fed and that is your ticket to Alkali carry, get fed by early banks as I already said and kill or assist it doesn't matter, you still get gold and Akali has an extremely expensive build with almost all of her items exceeding 3k gold.
Do not EVER give up on Akali, just stick to her and she will save you a lot. Always target the squishy champs first as you don't want to mess with tanks.
All in all have fun with Akali because she kicks ass and wrecks teams, I myself have carried countless games as Akali
and GOOD LUCK :D