Early game :

First you've to know that ahri uses her mana pretty fast with her spells, then you'll have to never spam them in laning harassment, just keep cool and harass when your opponent is coming to close to you.

Mid & late game :

In fight, you've to focus the carry of your opponents, your R permit you to run through the ennemy team to kill their carry. Use your Deathfire Grasp first to deal a huge burst, then Q, E, W and re use your ulti to try to keep safe, or use zhonya if you're in the quagmire.
Your Zhonya permit you to relaunch all your spells a second time during a fight, this is pretty awesome.

/!\ NEVER ENGAGE A TEAMFIGHT ! let your tank engage then go on the fight to kill the carries !
/!\ Try to survive as long as possible to deal more damages, do not go on melee fight against a melee fighter !