Ahri is a super fast mage-type assassin character. She is heavily dependent on your being able to land skillshots and by using my build, i assume you know how to do this. Otherwise, you might want to try one of those hybrid build that i know for sure are on the way (lol).
My build focuses on keeping you in lane and farming and getting built early on and transitions into a high damage, high survivability powerhouse build mid and late game

Marks- I take magic pen marks, of course
Seals- I take mana/5 seals to somewhat counter how mana-hungry she is. You may switch these for something else, because with my build, in late game you won't have any mana problems because you've been stacking your tear the entire game.
Glyphs- Yeah, these will somewhat hold you over until you start building some serious AP mid game, don't be too aggressive until you at least get your NLR (needlessly large rod) and WoTA (Will of the ancients). I also sometimes sub these for magic pen, which scale relatively well into late game, assuming the enemy is not building against you or another AP carry on your team.
Quintessences- Flat AP for your early game before you build much AP, can be subbed for movespeed quints. I love movespeed quints.

The items used in this build are typical, and always remember that item purchase is purely situational. Obviously, build against who you need to build against. And if you're doing particularly well, rush certain items, or if you're playing against particularly bad opponents, grab a medjai's. It's all very simple, really.

Do: Exhaust, Surge, Clairvoyance(If you feel like you need it, your support should probably get this though but you know how solo queue is.),
DO NOT: Flash (you have 3), Clarity (It tells everyone else "Hey look at me, I'm bad at conserving mana) AND ANYTHING ELSE

Last hit, last hit, last hit, last hit. Cannot stress enough.

Pros-
+ Good ganks if you can hit your skillshots
+ Great Burst and mobility
+ High survivability if played correctly
+High damage
+ Nice "fear"

Cons-
- Mana hungry
- Slow missile speed on Q
- No auto lock skills
- Very vulnerable to CC