The reason why I have exhaust and ignite as my spells (some people will call me nub) is because when you mid it makes it SO easy to kill mid. Once you hit lvl 2 and get shroud you can kill the opponent MID. I play akali to get fed and dominate the other team. This also puts into my reasoning of flat ap runes for early game. You will be so strong it's not even funny.

You find both of your hands glowing right when you spawn. This is what makes this build so great. You can spend money on boots to improve your chance of chasing and getting away instead of things to activate your passives. This is important: GO MID. I don't know if you have ever played Akali mid, or even thought about it BUT DO IT. I will now tell you why you are going to go mid. The hp pot you hold in your hands is for the threatening and fighting. Based on the character you are midding against it is almost always easy to q skill and throw a kama at them and back away before they hit you. The bonus is if they chase and want to engage, do this:(this is when you're level one and they are already hating you) Exhaust them (makes them hit you for like nothing), ignite them (damage and ap boost), consume the mark, throw another q skill because it should be off of cooldown by now, and then consume it again. By then, they will be dead. That's called a double nuke, as I call it. Basically anytime during the game, watch if they are marked. Mark them at all times, or try. Mark them, back off, wait for your mark to cooldown since the mark lasts longer than the cooldown, ult to them, consume the mark, and mark and consume them again. This is so effective it's ridiculous. Double nuking can take out more than half of their hp at any time. Your ult cooldown is less than 2 seconds meaning you can do this anytime you please. My simple harrass technique in mid is throw down w (shroud) and run towards the outside of it so they won't like sivir boomarang you, and then while you are invis, hit them with a kama. This is a very effective technique and after you hit them and they are still there, simply consume the mark. After you consume it your shroud will still be there so you can run away.

Gank side lanes when possible or when the team has over extended. Akali is very easy to gank with and when you combine the summoners that I recommend it's even easier.
There are also times you will have to be the one to initiate because your team is a bunch of *******. Try to stand at the side if a team fight seems to almost happen so if one of their team members tries to flank you will make them back with your nuke and slow. Then it will be a 4v5 :D

Pros
-Can tower dive
-Heals herself
-Nukes squishies very quickly
-Can chase like the best of 'em
-Can go invisible randomly
-One of the biggest nukes in the game while still having utility
-reliable damage
-can be scary AP carry
-If you don't do well early game you become strongest mid game so don't give up

Cons
-If you don't do well early game it could be hard to come back
-They will focus you so be careful
-Don't be over aggresive
-Can only nuke one champion at a time
-I don't see many cons

My items are all item per item on every game I play no matter what. If they have a lot of cc or magic, I will get the treads. If not, I'll get the boots of swiftness. That's the only way I change my build. If you are low on hp and they are chasing and faster than you it might be better to reengage and nuke them to heal up and you might live. Also use your shroud to slow opponents and help your team. The last item I have is rageblade. I like it because it gives you basically 86 or so AP and some AD and AS for only just over two thousand. That's the cheapest item in the game for what it does. It compliments Akali great as she is a combo champion.

A guide by top tier summoner that is very in depth that might also help : http://solomid.net/guides.php?g=8