Ahri scales quite well with AP so build that early. In no particular order, Luden's Echo and Morellonomicon are really good on her. Lich Bane is not exactly standard but it can work well and can be a lot of fun.
Ahri is best played like a kite mage, you want to avoid all in fights until you are in a good position and there is little risk to take for fighting. You can use Q to poke, and wait for an opportunity to catch an enemy with your Charm before going all-in on them.
When using Ahri's ultimate, it is better to hold onto it for repositioning purposes (you want to kite around enemies, each cast moving you to the edge of range so you can still deal damage) And rarely if ever should you dive directly onto a target with it.