Ahri's abilities are Orb of Deception, Fox-Fire, Charm and Spirit Rush (she also has a passive, essence theft, which gives her health on every 9th attack). The order in which you choose to level up these abilities really does depend on who you have on your team and against you in your lane. I usually pick Orb of Deception first, as this hits enemies twice and can be useful in getting those early kills. If you're playing against a highly maneuverable champion, I suggest charm as your second pick because it means you can orb then charm them- charm brings them towards you and if you're near a turret it can be one of the most useful moves in Ahri's skillset (it's also good to use when you're assisting other lanes as it can help the people on your side to get the kills). Obviously, with Spirit Rush being her Ultimate ability, you can only level it up at certain points. But once you have, Ahri really shows her usefulness- you can walk into pretty much any combat secure in the knowledge that you'll probably get out, or you can use it to get deeper into the action and hit 3 champions at once!
You have to build Ahri AP because all of her abilities utilise this. You can also build magic resist or magic penetration (resist if you're against a highly magic based enemy or are just being eaten, penetration if they've built magic resist because otherwise your attacks hit for very little damage). But ultimately, as long as you build her with AP from the start you can win very easily with Ahri. I'd suggest taking her out on a few bot matches before you play against other summoners, just to get used to her abilities and the best way to play them (it depends on many situations, because you won't always be playing against Annie or Ryze in mid, I've had to contend with champions such as Ashe and Yi in mid lane before).
I hope you enjoyed the spotlight!