Ok I'm going to teach you how to build Ahri and play her. The way you choose to play her is your choice. I will explain why I choose how to do each of these things. I will give my reasons why I chose my runes, masteries, and my items. This isn't an "Oh it's a build to play Ahri easy"! NO! With everything I am giving you, you need to play smart and hit hard.

Runes! The reason I choose AP runes and no CD or Mana regen is because I try to be precise. I can wait for when to strike that way I know I won't miss. On Ahri you don't want to freak out and throw your Q and E around like an idiot. You want to stay calm and be precise. I choose strong AP at the beginning of the game. Due to the fact that Ahri is ranged and it gives me a huge advantage. I know I don't have Magic Resist or Armor either but the 56 AP at lvl 1 is pretty good. Also your true damage! Never forget that. People say I'm stupid for having no defense but I can usually hurt the enemy before they can get close. What does it matter to me?
This build won't guarantee a win, but it will guarantee good dmg as Ahri if you can figure out how to play. I am trying to explain how to play her in this build as best as I can, so if some stuff doesn't make sense I truly apologize.

Alright Skill Sequence. You want to max your Q because it's the skill that does the most damage. You want your E at lvl 2 due to the fact you want be able to find an opening and hit them with it. W is such a bad poking skill cause you have to get close to them and with these runes and masteries you don't have much defense, but hitting them with your E brings them to you and you could be near teammates or a turret giving you such a huge advantage. You want to E then Q early game. At lvl 4 get your W and then turn that on if they get close enough. By the time you have your Q, E, and W. You should be able to kill the mid champ or whatever champ your aiming for. Tons of dmg early game with your Q + E and your W will actually do a bit cause they shouldn't be tanky yet and then you ignite. If they're surviving through the ignite give them a little poke with any of your skills. Preferably Q so they don't get away. ;) Now for the Ulti. This is so important and people waste it so often. You only use your ulti to run away or to chase a low hp enemy. You will never use it to initiate unless these circumstances come into play.
1. You know where all enemies are so you won't get ganked, because your R is your only true escape skill.
2. You know your dmg and you know your burst can kill the champion along with ignite.
3. You see an opening with E but you need your ulti to get into that position quickly without alerting the enemy champion. If you use this you should be able to do this well.
Uh on the skill sequence in the picture I may have messed up where to put them on what lvl, so just remember. Q first. E next. W last. R whenever you get a skill point that allows you to lvl up your R.

Alright last but not least the items. I start off with a dorans ring. Since I have those AP runes and AP masteries. The dorans ring starts me off with 56 AP at lvl 1. Imagine your Qs true dmg. It becomes much scarier as you lvl Q. You want to get boots next because since you already start off with a good amount of AP the magic pen will break their MR even more. It doesn't affect the true dmg I believe but imagine the first hit on your Q. The next item you want is a rabadons. You won't always get the kills so try to farm as much as you can too to get this. If done corrcectly you can get a needlessly large rod by lvl 6 or 7. The rabadons should come shortly after. The AP boost is huge and I'll repeat myself. Imagine your true damage and magic pen of your boots for when your Q first hits. The dmg becomes even more amazing. You want a rylais next because it gives HP and AP. You want more AP, but you also want a little more survivability. You may ask why not make a warmogs or Rod of Ages. Cause those won't benefit you as much as Rylais. It gives a good amount of AP and HP. You want an abyssal next due to the fact that when you hit them with your E they should walk close enough for your abyssal to kick it's passive in. The lowering of magic resist by 20. Since they get close to you through your E and the passive kicks in your Q and W should eat their faces open. Unless they're a tank of course, but if it's a carry you can just hurt them a lot. As they run you can ulti to chase them and the passive of your abyssal will be in effect meaning more dmg and you have a rabadons. Win win for you. If you play it correctly. Void staff is just to break through their resistance more. Magic penetration and 70 AP!? Sounds good to me. Now for your final item. Your Zhonya. Zhonya is good for when you are being focused. Don't use your ulti until after you use your Zhonya cause then you won't have an escape. Zhonya not only gives you armor and invincibility on activation. It also gives you a good amount of AP which your rabadons passive will increase. You should have around 500-700 AP. I don't remember, but you should be able to hurt them a lot. Don't be the initiator though, be in the back and poke them as much as possible in team fights. Use your E to bring people to your team. It's good to use your E to poke someone out of their team so your team can initiate. Especially if you E the carry. Since the person who got an E to the face will be helpless cause of what your E does.

Masteries. This one will be short. Check offensive and your runes and you've already figured out why. People might ask why not get some more utility. You only need that much mana regen if you don't spam your skills like an idiot. Plus the recall thing helps when you need to gtfo a bad situation fast.

These are a couple and I don't intend to show off. My friend's Riven build he made gave me this idea and I think it would help to show you if the results if you play smart with this build.There is a defeat there but that is on my teammates part. I was killing them all and we almost won, but remember you won't always win with this build. Your teammates will fail you or you will be having an off day, but this build shows that if you play Ahri correctly. You can get so many kills and most likely will carry if your team isn't stupid. ^^ Also take a look at the enemy Ahri's score and look at mine ;) See CD and Spell vamp won't save you~ :3

I thought it would help you more if I didn't just show you my gameplay. You can see how well it did for other people too.I gave my friend the Ahri build and this is how she did when she afked for like 5 - 10 minutes. I taught her this build and how to play Ahri. :)Here is another game of my friend carrying. This time she took the screenshot for me.

Thank you for taking a look at this build. Please vote and give feedback. ^^ I'd really like to see how well you guys like this and if it helped you. If it didn't then I apologize it isn't to your taste ^^ Anyways as they say in game. Good luck and Have fun! :3