The Mark of the Assassin buff lasts longer than the cooldown, allowing Akali to cast a Mark of the Assassin followed by Shadow Dance. Finishing with another Mark of the Assassin gets extremely high bursts of damage.
Due to low cooldowns of Akali's abilities, constant usage of Mark of the Assassin can easily make sure her energy issues are dealt with. This also applies to healing early game, due to her Innate's Spell Vamp.
Due to the movement speed reduction of Twilight Shroud, it can be used offensively to provide cover and allow chaining skill combos on the enemy faster, but can also be used defensively to prevent drawing enemy focus during team fights and to provide aid in retreating after a team fight or running from a gank.
Twilight Shroud is great for running from enemies in the jungle, especially near brush, and for checking brush for enemies.
Using Twilight Shroud followed by Flash to go over a wall can effectively confuse enemies and following up with a Shadow Dance will create distance between enemy's in pursuit of Akali allowing her to escape with ease.
Crescent Slash is great for farming gold and pushing lanes.
Once you hit your first 3 stacks of Shadow Dance, look around the map for an easy gank. This is the time where Akali starts to truly shine
Starting off with a Long Sword or Amplifying Tome is useful because it will activate her passive.
Akali can deal massive damage with Lich Bane combined with her passive and auto-attacking needs of Mark of the Assassin.
Runes and Masteries can be utilized in order to immediately activate her Innate. Combined with the Ignite mastery, she may, with base 10 Ability Power and a Doran's Blade, get both Disciplines up at level 1. This can be helpful if you want to start with boots and pots instead of choosing a passive to start with.
Even without the necessary Runes and Masteries, Doran's Blade is a good choice for a starting item in any build: together with her innate, it provides Spell Vamp, Lifesteal, and Health - all which will aid staying in lane longer (as well as Attack Damage).
Purchasing Mejai's Soulstealer or/and Sword of the Occult early can make you really powerful late game if you are able to earn a decent number of kills without dying. Though these are amazing items for her, they are situational, solely relying on your early-game performance.
Guinsoo's Rageblade and Hextech Gunblade are great item choices to Akali for their AD and AP boost if you are building her as a hybrid.
Rylai's Crystal Scepter is a great item to get because the slow is applied with her Mark of the Assassin and Shadow Dance allowing her to stick to her target better and reducing the chance that he/she gets away. The health also helps keep her alive longer. SINCE WE HAVE ATTACK DMG RUNES AND MASTERIES DON'T BUY ATTACK DMG ITEMS TO START