hi, just to let you know i'm not a pro but i'm here to share my experience on akali and to give you some quick understanding on this champion. in the past akali is one of my strongest champ(not anymore), not because she is OP(over power) but because i know how to play her and to adapt to the team and the situation I'm facing...

PROS:
+ SEXAY
+ can take down an adc, mage within a blink.
+ great at juking/escaping
+ easy to play
CONS:
- Hard to fully master
- Fall of hard in late game
- Item dependent
- not good in team fight, if you land the dome where it shouldn't be

in this chapter, this is the most IMPORTANT information and i recommend you to read this CAREFULLY and try to understand what I'm trying to explain and what you should buy and not to.
Boots of Swiftness: why? why not buy counter boots or magic penetration boots, well for me to play Akali well you must be able to chase the enemy and being able to escape when needed and to be able to do that i must have a boots that will give me higher movement speed than other. and Boots of Swiftness suites my demand. if you are going against high magic resist champion i recommend you to buy magic penetration boots and then replace it with boot of swiftness when its not laning phase anymore or when you have the damage item to replace the magic penetration boots.

needlessly large rod: another weird items to start with Akali. i know i know... you might think that this will not work with her but wait, most of the game i play i usually buy this item in laning phase(early game) since this items gives me 60 ability power!!! if you add up the AP runes and this item together it would be a nightmare for the opponent especially squishy top champions like Teemo and Elise. your q damage when you obtain this item would deal around 200-400 damage which is already a lot of damage in early game plus the trigger which is 200-400.

Hextech revolver: many Akali player start with this item because its sustainable, give you AP and if you collect money and turn this into Hextech gunblade its nearly impossible to slain you unless its 3v1.

farming, last shot minions, these things is essential for MOBA player. this skill can be obtain by practicing. in early game it is very important for you to slain as much minions as possible to take advantage of your opponent. Akali is a very good farmer. her E deals AOE damage (area of effect). Akali also have her Q which deals incredibly high i mainly use her Q to harass enemy and to zone them from farming and to destroy tanks minions