Pros:
-High Mobility
-Heavy Burst and Scales Well
-Strong in Lane
-Lots of AoE in team fights
Cons:
-Squishy
-Easy to learn hard to master-esk
-Mana Problems and therefore each skill you make must count
-Does not really provide too much to the team besides assassinating carries which means that your positioning is key.

Your basic Combo is E, Q, W or you can do E, W, Q. Honestly it is a preference.

vs Ahri:
I personally do something that is very unorthodox at the start of the game which is get boots 4 due to the fact that I play passive in a mirror match up and with the extra movement speed you can dodge most of the other Ahri's skills. However this is definately not recommended, so take Doran's 2 Hp
vs. Akali:
Akali before 6 is almost laughable to play against. However when Akali does hit six you have a major advantage. When Akali Qs you then jumps on you with your Ultimate, just combo her, E W Q, then half health is gone, However if you feed an Akali in lane its pretty much GG because R-kali snowballs extremely well, feeding one kill is not a big deal just be sure to play passive after that and communicate with your jungler.
vs. Anivia:
SOOOOOO EASY, Just farm, don't play agro at all due to the fact that she has her egg which negates your aggression. However, if you have a chance to burn her egg do it because she is so squish, even if you pop ignite to get the egg down, its down for 240 seconds, your ignite comes back in 210, which means you have a a 30 second time window to kill her with ignite. Once ignite is up again for you, take that opportunity to burst her down.
vs. Annie:
This lane is very tough and you may have to have to face it even though Annie is more used as a support than a mid. However, if she goes mid then play really passive until out of laning phase. My preference is that I stay passive and build magic resist (negatron cloak: the Athene's route is an option as well or both). Annie's stun is very deadly, left click on her to see the status of that stun. Also, considering the fact that she has a large amount of base damage + AP = death to the best champion in the game. So, build mr, stay passive, communicate with your jungler so he can gank which is very beneficial considering the fact that she has no mobility besides her flash and stun. When the jungler comes to gank, bait her stun and go in >:D.
vs. Brand:
Brand is tough to lane against, but Ahri outranges him and you can poke him down easily, just dodge his w's and you should be fine in lane. Brand's damage hurts but considering his squishiness, you true damage can other forms of damage hurt even more :).
vs. Cassiopea:
Very annoying lane to deal with due to DoT. However considering the fact that Cassiopea is not played that much not due to her AP scaling but because of her kit. Her kit out of lane is really bad, she has no mobility, you do. Don't all in her with your ult because her ult negates your all in. Build some magic resist if you are struggling and POKE her not all-in her. Once you are out of laning phase, she is pretty easy to deal with in my opinion.
vs. Diana
This match-up is actually surprisingly tough. Diana's AP scaling is pretty strong and she can snowball fairly well. During laning phase she is pretty tough to deal with. Bully her until 6 but then just farm and dodge her Q's. If she jumps on you, she can deal a lot of damage to you that can be the end of you. Out of laning phase, Diana will do pretty well in team fights so use your ult for positioning and don't go balls deep because Diana will punish you for that.
vs. Fizz
Very tough lane because Fizz's E negates your charm. So, in this lane, Let Fizz come to you. He will do his basic combo on you, Q, W+AA, then E's out. Keep track of when he uses his E and also harass with your auto attacks. The ONLY reason that Fizz is going to be aggressive is to allow him to safely farm and possibly kill you. Fizz's E has a cooldown of 10-15 seconds early on which gives you a window in order to be agro towards him. Land your charm, q e, half health gone. If you are starting to struggle versus him, Gank other lanes which allows Fizz to take your Tier 1 and then you can Free-Farm at that point. Also be weary of his Shark because that's when Fizz all-in's you. In Team fights, again use your ult for positioning because chances are Fizz is going to be focusing you or the ADC. Therefore your ult can peele for yourself and/or your adc.
vs. Galio
I'm going to be honest, this lane is like facing an immovable object. Galio is going to be building flat magic resist and also using his shield to heal the damage you deal to him. While he is annoying in lane, he is not as strong as you out of Laning phase. Gank other lanes and farm, that's the name of the game.
vs. Gragas
Please, not after those nerfs. You hard counter him.
vs. Heim
Play passive. Gank other lanes. His turrets hurt and you can't really stop him. Sac your tier 1 and free-farm. Out of laning phase, you will destroy Heim. Just don't be in range of his Ultimate turret because that turret HURTS so much.
vs. Karthus
GG. You win.