This is my knowledge of League of Legends with Ahri.
And I want to share with you what I know and also hear some feed back from your experience so that we can learn from each other and know more about this game time will change over time.

Here is my Guide to playing Ahri (for me).

P.S if there is anything I say which is wrong (except my opinion) then feel free to tell me!

Early game you want to make your opponent farming phase difficult.

By not letting him farm without sacrificing something. One way is to prok thunderlord when he tries to farm by auto attacking and Q. Yout Q cost quite a lot of mana if you spam it, therefor you should only use it to prevent him from getting keys farms e.g cannon turret is low, 2< minion are low or when thunderlord is up.

Another way to prevent your opponent to farm is if they are not behind a minion you can E and Q which will be as effective as it proks thunderlord but will cost a lot of mana and you want to always have E up before level 6 as it is a great ability to dis/engage.
A cheaper alternative is to E ,W and auto attack which should prok thunderlord.

The whole point of this is to scare your opponent and not let him farm so that you can get a fundamental advantage.

NOTE: Try to only push before level 2-3 and after level 6 as between these level jungler could gank and you will have no escape.

Like most champion you bring FLASH as it is a good spell to dis/engage, also with ahri's ult you can do much more as it gives you more mobility to your kit.

Here you can have one of these Spells:

IGNITE: Most common spell you will use with Ahri as you want to snowball in the early game. Once you get level 6 and your opponent is decently low you can do your combo which will usually get them very low and so ignite will finish them.

CLEANSE: Is useful against people who have hard CC during laning phase and can burst you down during the time you are stunned e.g Annie, Twisted Fate.

EXHAUST: You will only take this when your opponent require to burst you by going all in on you e.g Zed, Talon.

TELEPORT: You only get this when you have a tough laning phase and that you know you can not kill your opponent early game OR if you are going to ahri (which this Guide does not cover).