I am still improving this guid so thanks for all tipps.
I'm testing some changes right now so be a bit patient changes will come.
Thanks to exitfeat, BloodyNine and wolfstray64 for their help!

HELLO GUYS!
I see you've decided to play Akali the Fist of Shadows.
For introduction I'd like to say this is a very good choice, she's a nice char
making some EPIC burst Damage.
So before starting the Guide I'd like you to know that this is not obligatory
this should just show you one possible way how to play her which suits me best.
So here another tipp: Start playing Akali with a build you like(maybe this one ;) )
and then change this build, try some things and find your own way to play her that suits you best.

Pros:

Just like I already said EPIC burst Damage
One of the best Anticarrys
Unique instant invisibility Ability
Genius Ultimate
Great in chasing enemys

Cons:

Low life and defense
You will be focused often
If forced to play defensive really weak

Well first I'd like to start out with the offensive Masteries:
[*] The point on ignite is pretty important since you really want to finish of your enemys and since you definitely will use your ignite the extra 10 AP really will come in handy.
[*] Also very important, since Akali relys very much on her AP the point on Archaic Knowledge which gives you amazing 15% meigic penetration.
Now off to the Defensive Masteries:
[*] due to your lack of life you will really want the full points on Veteran's Scars and Ardor so rally get them!
the rest is mainly up to you!

Your main skill is of course your Ultimate which is quite amazing because you can use the 3 times in a row so always take it if possible.
Followed by your Q skill which is also REALLY fantastic because it can make damn much burst damage, in fact it will be your main killing Ability, so this is like the first skill you will want to finish!
Your W skill is quite good to scare away your enemys and get some minions for free so you should get one point on it on level 2 but its not wrth more up until the end, so just let it be and finish it last.
Your E skill is your only AOE one so it is pretty usefull for Farming and getting some money, its also a good combo used together with your W skill. Finish it second ;).

Get the 3 Marks of Strength for some additional start damage and for getting your first passive skill.
I've skilled all the rest of my runes on AP for extra Mark damage couse it all doubles if you hit the enemy within the 6 seconds and your Ultimate also improves!

Start with Longsword for additional Attack(You might make Sword of the Occult out of it in the end but in most cases you wont get that far) and one potion.
try to stay on lane until you get 1000 gold to immediately purchase your boots if you get low life you might also purchse the normal boots first and go for your final boots later.
After that stay on lane til you get 860 at least and purchase the Blasting Wand.
Now get for some extra money, get some kills and farm a bit until you get 1460 at least and purchase two kages (you might also purchase them one after another) than go for another kage as soon as you can.
Now you should really get money like hell!!!
Wait until you get the required 2245 or so and improve the Blasting Wand to Rylai's Crystal Scepter which will help you survive and get loads of kills since you can slow the enemy down with your Abilities now.
Next wait for the required 1260 and sell one of your preciouse Kages for Sheen.
Wait again until you have enough to make a Lich Bane out of your Sheen.
After that you should really be hard on your enemie's team even able to take out some tanks on your own if you know how to play and the game should almost be over, if not fnish it by selling one of your Kages again to buy the Needlessly Long Rod which you will improve to Rabadon's Deathcap and if even thats not enough do it again, that you have 2 times Rabadon's!
Now noone will survive if you go in!

Preamble
How to kill with Akali:

Try to hit your enemy with aour Q skill to get a mark on him.

Wait 1-2 seconds

Bash towards your enemy with your R skill.

Place another Mark on your enemy with your Q skill.

Autoattack your enemy, watch whether the enemy can get away or not, if he can try to finish him off with your R skill before he can!

Your enemy is getting away?? He reached a tower?? look how much damage you dealt to him and see weather you can finish him and flash out of the dangerouse Tower zone.

If you have used all your Marks and Essneces try to slow down your enemy with the W skill and then deal some extra damage with your E skill.

Early Game

Look out for your life better go home than die!

Scare your enemys away using your W skill to prevent them from Farming.

Farm as much as you can

Mid Game

You should have Rylai's Crystal Scepter by now and try to go for a gank.
Go for the weaker Carrys such as Ashe.

In Teamfights always pic the weakest enemys and finish them using R or Q->R depends on how much life the enemy has

Do not attack the Tanks unless you're REALLY sure you can get them

End Game

You should now have at least 450 AP and, if you can value the circumstances, be able to take out some tanks but be careful!

Remember, you're an Anticarry so support your team by taking out even more carrys and go for the towers/baron!