Abilities

Twin Disciplines:
Akali's passive is what makes her a viable hybrid. She gains bonus magic damage from AP and spell vamp from AD. With flat AP and AD runes+3/3 Brute Force, both buffs will be activated at level 1.

Mark of the Assassin:
This is Akali's main damaging ability. Max it first. Use it to harass early game. Whenever it's safe to fully engage, wait until the cooldown is up to burn the first mark and afterward use it again for a double auto attack double mark burst. Deals tons and tons of magic damage, fast.

Twilight Shroud:
This is Akali's stealthing ability, unique in that it is the only stealth that activates instantly. Use it in the thick of a teamfight, for zone control, to juke, to 1v1 kite, to slow enemies, and for facechecking brushes. Be advised that it starts at 80 energy, so be careful when using it while bursting. Use it at the edge of brush or around a corner to juke. Flash out of it when death is otherwise imminent. Also don't forget that it gives Akali armor and magic resistance, so it just might save you from that DoT or turret shot.

Crescent Slash:
This is Akali's only AoE ability. Use it for farming and bursting. Remember that its range is very short and easy to miss on fast moving targets. It scales off both ability power and attack damage, but only does physical damage.

Shadow Dance:
Akali's ultimate is what defines her. You can do so many things with this ability. Start off a surprise gank with it, last hit that about to die creep, chase and kill steal like a pro, burst with surplus charges, and most importantly, juke. Does a surprisingly large amount of magic damage.