Ahri is, by my opinion, one of the weakest champions in the game. So by standing closer to your turret and farming, you can watch how your enemy in lane plays. If you just farm, the enemy will not suspect you to poke or go in. So when he don't suspect it, go closer and poke him. Once you get your Q, W and E up you can start looking for openings to E, then W and then Q.

Once you get your ultimate, you can farm like nothing is gonna happen and try to poke him to half of his HP. When he really don't expect you to, you dash into a position where you can E, W and Q. You have 3 dashes, and those 3 take dmg if you dash into him.

The basic attack doesn't do much dmg. So last hitting is important. Let the minions poke and then you can last hit.

The E can distract an enemy from a teammate that is low. The E makes him run slowly after you, and then allows your teammate to get away alive.

The E lets you distract the enemy, and can even stop others ultimates like Miss Fortune,
Warwick, Lucian, Katarina, Jhin and Xerath. If you hit the enemy you're gonna be focusing, the chance is big that you win the teamfight.