I have played a lot of games with her and i got good results. She is skill-shot based so to play her you will need to practice to land all of your skillshots. I play her mostly in mid because i think its better for her.This is my first guide i hope you like it.Rate it and leave your opinion to let me know if the guide is good :).
PS: sorry if i have bad english im not american.PS2: im still updating this guide with images and more explanation.

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I go 21/0/9 Taking 3 points in mental force, 4 points in sorcery , 1 in arcane knowledge, 3 havoc, 4 blast,4 archmage, 1 executioner in offense tree.And in the utility tree i take: 3 expanded mind, 1 improved recall, 3 meditation, 1 runic affinity.I master ignite and flash in the respective trees.

She is a burst AP assasin, all her spells scale with the amount of AP you have so you will need in the offense tree all the masteries that boost the damage of your spells.
The rest of the points are in the utility tree i take mana regen because she spam her spells and if you use them too fast you will run out of mana in no time. I also take the expanded buff duration if you get blue it will stay longer with you.

For Runes i use:
Greater Mark of Magic Penetration x9: Magic penetration marks are always importan in AP champions, because there are a lot of armor penetration items but there are not enough magic penetration ones, magic pen runes make you hit harder with your spells.
Greater Seal of Armor x9: all the casters have problems with heavy dps with gap closers this runes will make you survive more to their ganks if your ultimate is on CD and someone caught you.
Greater Glyph of Scaling Ability Power x9 : Ap per level glyphs, these gives a nice amount of AP , in early game flat ap glyphs are better but ap per level gives much more ap in mid and late game.
Greater Quintessence of Scaling Ability Power x3 : More AP per level runes, like the glyphs per lvl these gives you large amount of AP in mid and late game.

For sumoner abilities i take:
Ignite: I take it because this helps you in your burst to prevent healings and can finish your opponent if he manages to escape from you with low hp.
Flash: You already have 3 flashes with your ult but when it is in cd this can help you to escape or chase to land a spell.
Other spells you can take[bold/]:
Ghost: If you think 3 flashes are enough and you want to get to a turret faster, chase enemies and get a nice speed to escape from a bad situation.
Surge: This spell at higher levels gives you great amount of AP (max AP = 86), if you want more burst chose it and activate it before you use all your combo. It also increases your AS so you will have some extra auto atacks.
Clarity: If you play too agressive you will run out of mana, if you think you will be agressive use it but i dont recommend it because if you use your spells well you shouldnt have mana problems.
You can change Flash for any of these spells.

Essence Theft
Passive
Ahri gains a charge of Soul Eater whenever one of her spells hits an enemy (max: 3 chargers per spell). Upon reaching 9 charges, Ahri's next spell has a 35% Spell Vamp.

This is a really useful passive and will make you stay in lane longer.
Use orb of deception to stack it and to use it.


Orb of Deception
Ahri sends out her orb, dealing (40/65/90/115/140) (+(0.33 per ability power point)) magic damage, and pulls it back dealing (40/65/90/115/140) (+(0.33 per ability power point)) True damage.

The main damage you will make is with this ability. Use it to stack your passive and when you reach the 9 stacks use it when the minions are coming so you can hit all of them.


Fox-Fire
Ahri releases three fox-fires. After a short delay they lock on to nearby enemies (prioritizes champions), dealing (40/70/100/130/160) (+(0.38 per ability power point)) magic damage. Additional fox-fires that hit the same target deal 50% damage [max damage: (80/100/120/140/160) (+(0.75 per ability power point))].

With this and with orb of deception you can reach the 9 stacks in just 3 abilities.
It doesnt do a lot of damage to a single target because in teamfights you dont know where the foxes are going.


Charm
Ahri blows a kiss dealing (60/90/120/150/180) (+(0.35 per ability power point)) magic damage and charming the first enemy it hits, causing them to walk harmlessly towards her for (1/1.25/1.5/1.75/2) second(s).

A good taunt this will be your initiator when you want to kill someone, its a skillshot so you need practice to land it. At lvl 5 the taunt is of 2 seconds that is enough time to release your combo.


Spirit Rush
Ahri dashes forward and fires essence bolts at 3 nearby enemies (prioritizes champions), dealing (100/140/180) (+(0.3 per ability power point)) magic damage. Spirit Rush can be cast up to three times within 10 seconds before going on cooldown.

Her ultimate, it does a good damage, help you chase your enemies, escape from ganks, and helps you to find a good place to shoot your skillshots while doing damage.

Soul Eater (passive)

If you learn to use this you will stay in your lane until you want to go back. Using this in a appropiate way you can heal all the damage your opponent is trying to do. You can stack your passive while harrasing and farming. Using Orb of Deception you can get 3 stacks really fast, then use Fox-Fire and you will have another 3 stacks, finally use Fox or your orb to reach the 9 stacks.
When you reach 9 wait until a new minion wave comes, when the minion wave is in a straight line coming use your orb to hit all the minions so you can heal you all you can.

Orb of Deception ( Your Q )
This is your main damage ability if you manage to hit 2 times with it. Remember that when the orb returns it makes True Damage :D.You should harras the with this while hitting the creeps to last hit. It has a nice range so you can cast it from behind your caster minions but remember that if you are too far the enemy will have time to avoid it.Use this to heal yourself with your passive.

Fox-Fire (Your W)
This spell has good damage and its not a skillshot but you dont know where the foxes are going because they prioritize champions but in a team fight you are not going to be sure if they are hitting the tank or the carry.In lane phase is easier to land it because if you go near your enemy you will hit him with the 3 foxes. (each consecutive fox deal 50% less damage) You can use this to pop an enemy Banshee's Veil

Charm (Your E)
My 2nd favorite skill of ahri (1st one Orb of Deception :P) Its a long skill shot taunt but you will need practice to land it correctly. Its the initiator of your combo so if you want to hit with all your spells you cannot fail this taunt.If you are against a melee (its strange to see a melee in mid but there are games when an auto-atacker is mid) to last hit minions he will need to walk to the front of his minion wave in that moment when he is about to last hit use Charm then use your Orb of Deception with Fox-Fire, do this every time he tries to last hit. If you are against a caster use it when they are out of place.

Spirit Rush
3 free flashes and great damage to 3 champions with each dash. With this you can chase someone to taunt him, escape from ganks and to do damage to the enemy team while you focus their squishiest champion with the rest of your combo.It can help you dive turrets easily, just harras with your other spells and when he is low hp you use your combo and dash against him if he runs to his turret dash again to get him as low as you can (or kill him) and use your Ignite to finish him, use the last dash to escape from turret range.

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Maxing Q first: I max Orb of Deception first because its a great harrasment while you are farming and the damage helps you a lot to heal yourself using the passive.
Maxing W second: After the orb you should take Fox-Fire because it has a really nice damage and at lvl 5 it has a low cooldown so you can use it faster.
At last your E: Finally you should upgrade Charm It has a good damage and a taunt that increases with each rank but with 1 sec is enough to pull your combo and with lvl 5 you will do more damage.

Doran's Ring Sorcerer's Shoes Rylai's Crystal Scepte Rabadon's Deathcap Will of the Ancients Void Staff
This is how your full build should be. I have testing an alternative item that you can buy before Rylai's Crystal Scepter and is a Deathfire Grasp, the active its a great addition to your burst and it gives you AP, CDR and 10 mp5.
If the game is still going after all this items you can change your for a defensive item if you need like and or more armor with a good amount of AP
If the enemy team is stacking magic resist you can change for a
Once you get your you can start buying Elixir of Brilliance for the AP and CDR it gives.

I will name the champions you can face in mid lane and how to play against them. Even if you see here a non-mid champ its because in a game i have faced that champion in mid. (i will be updating this section)
Annie: Like with all the other champions when you see annie with her Pyromania charged you dont go melee range with her. Start last hitting and you will find out if she is a smart annie or a bad annie, if she is smart she will use Disintegrate only to last hit and she is not going to try to harras you and will avoid your orb. If she isnt smart she will try to harras you, remember that it hasnt a long range so when she gets near use and and she will run away, this work when she tries to stun you too. When she hits 6 avoid to be low hp or she will flash and release Summon: Tibbers and you will die.
Ashe: Use your orb to harras her but dont waste mana using it like crazy, stay behind minions to avoid Volley and you will be fine. When you hit 6 and you are sure you can kill her use your ultimate to position yourself for a taunt but be sure you will hit her with ult and as fast as you can ult again in zig zag following her to avoid her ultimate Enchanted Crystal Arrow activate Fox-Fire and Orb of Deception with Ignite by now you should be receiving the first turret shot if you cast your spells fast, if she is not dead ult again and ignite or the shot will kill her and you should be safe going back to lane.
Brand: Most of the brand users try to push their lanes with Pillar of Flame and starting to do dmg to your turret easily because when you are behind turret they will zone you with pillar, if you see he is doing that then do the same thing with your hit all the minions and you will push faster, when you do this also try to hit him with the orb or in the way back positioning yourself. Stay at the side of your caster minions to avoid the pillar and when he use you can harras him because if you want to go in front of him he will stun you and you die. When he hits 6 if he tries to flash and release his full combo if you dont feel fast enough to cast your taunt flash away or use your ult and hit him then you can use the rest of yur spells.

At lvl 1 just try to hit the whole minion wave and maybe the enemy to get stacks on your passive, auto atack only to last hit the minions.When you get lvl 3 dont try to use your full combo because u will run out of mana really quick, just keep using orb to harrass and auto atack to last hit if you use the orb correctly u will start hurting him and you are not going to lose a lot of mana. If he is beside the minion wave you can use taunt and then orb to do more damage, if he is behind just use orb.Lvl6 this is the moment when you can be more agressive, keep harrasing with orb, and if he is half hp you can use your taunt then orb and use ult the get closer and activate fox fire and ignite and dash 2 more times.
If you see that your team needs help in a lane you should go and help them to push their lanes faster.

Remember you are ranged and all your spells have a nice range so please dont use your ult and go to the middle of the fight as soon as the enemies atack you need to see and place yourself in a good because if you are focused you will die in a few seconds.First you need to use Orb of Deception and try to hit all the enemies, then look at them and choose someone ( the squishy one) to target with Charm, it has a long CD so maybe you are going to use it only one time in the battle so you need to choose the perfect target (either to kill him or to defend your carry by taunting). Next thing you should do is activate Fox-Fire to do more damage to them, this spell has low CD so use it every time with your orb. Finally use your ultimate Spirit Rush and try to use the 3 hits per dash to finish the enemies.

Thank you for reading my guide, i hope you liked it. All the opinions are welcome, help me no make this guide better telling me your points of view.