Ignite: I always take it because, it not only makes akali more scary to go against, but it also adds a little more magic damage to her and could kill squishes that try to run away with barely any HP.
Flash: This is a great escape tool for Akali, due to the fact she might get stuck in tough situations. This could be the key to getting out of them.

Passive: This is her unique passive and what it does is it give you two little buffs. One is for magic damage and the other is physical damage. You know that you have them when you see a green and red glowing effect on your weapons. It also tells you the percentage of the amount of extra damage you will get.
[q] Mark Of The Assassin: This should be your first skill to get as it is great for last hitting minions, but not only that, Mark of the Assassin is your main source of damage. When you hit someone with it. It will show her small weapon spinning on top of them where you should hit them with a auto attack that will release a lot of damage onto that person.
[w] Twilight Shroud: is her stealth ability. It unique for you have a small circle to stealth around. It also comes with a slow when champion's or minions run over it. It's helpful for getting out of team fights when they don't have oracles to see you in the shroud.
Your text to link here... [e] Crestcent Slash: You should never get this skill first, because it doesn't do a lot of damage to the opposing team. It better for clearing waves of minions, but it also wastes a ton of energy. What the skill does, is you spin in a circle fast enough to do damage to whoever is around.[r] Shadow Dance: This is her ultimate and what it does is allow you to jump fowards the opposing champion to damage them and do another round of her combo. It's like a mini flash.