Ahri is a considered a high-mobility assassin mage. I find this to be a fairly accurate description - despite what others may think. She's a monster if you build correctly and can land skill shots. If you cannot land skill shots often (and I find her's to be pretty easy to land) you will get mopped.

This is my first guide, so be gentle!

Ahri, The 9 Tails Fox
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Unlike other foxes that roamed the woods of southern Ionia, Ahri had always felt a strange connection to the magical world around her; a connection that was somehow incomplete. Deep inside, she felt the skin she had been born into was an ill fit for her and dreamt of one day becoming human. Her goal seemed forever out of reach, until she happened upon the wake of a human battle. It was a grisly scene, the land obscured by the forms of wounded and dying soldiers. She felt drawn to one: a robed man encircled by a waning field of magic whose life was quickly slipping away. She approached him and something deep inside of her triggered, reaching out to the man in a way she couldn't understand. His life essence poured into her, carried on invisible strands of magic. The sensation was intoxicating and overwhelming. As her reverie faded, she was delighted to discover that she had changed. Her sleek white fur had receded and her body was long and lithe…the shape of the humans who lay scattered about her.

However, though she appeared human, she knew that in truth the transformation was incomplete. A cunning creature, she adapted herself to the customs of human society and used her profound gift of beauty to attract unsuspecting men. She could consume their life essences when they were under the spell of her seductive charms. Feeding on their desires brought her closer to her dream, but as she took more lives, a strange sense of regret began to well within her. She had reservations about actions which never troubled her as a fox. She realized that she could not overcome the pangs of her evolving morality. In search of a solution, Ahri found the Institute of War, home of the most gifted mages on Runeterra. They offered her a chance to attain her humanity without further harm through service in the League of Legends.

"Mercy is a human luxury…and responsibility."
-Ahri

Damage 50 (+3 / per level)
Health 380 (+80 / per level)
Mana 230 (+50 / per level)
Move Speed 305
Armor 11 (+3.5 / per level)
Spell Block 30 (+0 / per level)
Health Regen 1.1 (+0.12 / per level)
Mana Regen 1.25 (+0.12 / per level)

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

(Q) Orb of Deception - Ahri sends out and pulls back her orb, dealing magic damage on the way out and True damage on the way back.
Ahri sends out her orb, dealing 40/65/90/115/140 (+0.33) magic damage, and pulls it back dealing 40/65/90/115/140 (+0.33) True damage.
Base CD: 7 sec
Cost: 60/65/70/75/80 Mana
Range: 880

(W) Fox-Fire - Ahri releases three fox-fires, which after a short delay lock on and attack nearby enemies.
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) magic damage. Additional fox-fires that hit the same target deal 50% damage [max damage: 80/140/200/260/320 (+0.75)].
Base CD: 9/8/7/6/5 sec
Cost: 60 Mana
Range: 800

(E) Charm - Ahri blows a kiss that damages and charms an enemy it encounters, causing them to walk harmlessly towards her.
Ahri blows a kiss dealing 60/90/120/150/180 (+0.35) 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).
Base CD: 12 sec
Cost: 50/65/80/95/110 Mana
Range: 975

(R) Spirit Rush - Ahri dashes forward and fires essence bolts, damaging 3 nearby champions. Spirit Rush can be cast up to three times before going on cooldown.
Ahri dashes forward and fires essence bolts at 3 nearby enemies (prioritizes champions), dealing 100/140/180 (+0.3) magic damage. Spirit Rush can be cast up to three times within 10 seconds before going on cooldown.
Base CD: 80/70/60 sec
Cost: 100 Mana
Range: 450

Get Orb of Deception and max it first. I like to get charm and max it second because of how useful it is (adding more time to the seduction) as well as doing dmg. I grab one rank of Fox-Fire at lvl 4 for extra dmg/harass and max it last. Going this route requires you to be able to skill shot... but that's why you're all here, right!? Ahri is a skill shot champ and needs to be played like one.

Ahri's Orb of Deception is fast so it's easy to hit, and does true dmg on the way back. Thus for harassing, it's good to hit the enemy close to max distance so it's near impossible to avoid the damage on the way back. Also use this on lots of minions when your passive is up to get the most health back. Used constantly for farming as well.

Fox-Fire I find the most useless ability. Sure it does some damage.. but it's close to a pitiful amount, and it has no utility at all. Basically just pop it to deal more damage to enemies near you.

Charm is what I believe really will make or break good Ahri players. Land this correctly and it will instantly turn the battle more in your favor... miss it or use it carelessly, and it can be the cause of your downfall. It's an extremely powerful ability, with a pretty low CD - part of the reason why I feel Ahri is a bit over-tuned at the moment. Use it on people who tower dive you, to capitalize on the enemy team being out of place (ex: the carry is out front... snag em), to save yourself if someone gets on you in a team fight and you don't have your ult up. DO NOT use it to pull the enemy team's initiator to you, do not use it to pull a champ to you when you're trapped, and don't use it to farm.

Spirit Rush is why Ahri is considered to be high-mobility. A fairly short CD for essentially 3 flashes that deal damage to up to 3 enemies around you. This basically has all the uses of a flash and more. Use it to kite people, burst them, escape, position yourself, and to dodge. That pesky trynd about to spin over the wall? Save a charge or two to chase him (2 if you need to get out afterwards). Insanely good ability which should keep your deaths low and your kills high! Also decently low cool-down.

I use Greater Glyph of Ability Power, Greater Mark of Magic Penetration, Greater Seal of Armor, and Greater Quintessence of Health for glyphs.

My personal play-style is to destroy my enemy early game to the point of no return for them. I believe this rune set-up helps accomplish that. Magic Pen is obviously a great choice for an AP carry for more damage, Starting with near 10 bonus AP does more than most people realize early game, armor helps mitigate damage, along with health to let you have an edge on your enemy (since you are bound to be near enemy champs if you're getting kills). This rune set-up makes you capable of pushing your lane, killing the enemy champ, and a bit of sustain - allowing you to out-level your enemy. Those tempting tower-dives are also slightly less threatening to your life!

I realize other players do not have the same play style or thinking I may have. Thus other great runes are Greater Quintessence of Ability Power and Greater Seal of Ability Power: for maximum early game damage, Greater Glyph of Scaling Ability Power for more mid- and end-game damage, or Greater Seal of Vitality/ Greater Seal of Health for more survivability.

I have found that Ahri does not have any real mana problems when getting Rod of Ages first, thus not needing mana or mana regen runes. Her cool-downs are also very short, waiving the necessity for cd runes.

Ignite is great for Ahri, as she's an AP champ with great chase/escape and she's fairly short range. Ignite adds a little more damage as well as halving healing on the enemy - I wouldn't play without this on Ahri.

Ghost is the other spell I use on her. She has 3 built in flashes - there's no real need for Flash as well. Ghost allows her to chase/escape even better, it compliments her high mobility very well.

Other choices:
Cleanse may be viable if you find yourself against a heavy cc-team or you just seem to get yourself in sticky situations a lot.

Flash is always good if you are not used to her ult yet, or if you just like the comfort of knowing you have a 4th flash if needed.

I rarely consider anything else, seeing as the other summoner spells either do not have synergy with Ahri's kit, or are down-right useless.

I use the standard 21 points into offense for AP carries. I would recommend the utility tree for the secondary tree for Ahri. Expanded Mind is the logical choice for mana-based champs, and my preference is the extra point Good Hands , but reduced cast time on recall can be useful, or even flash cd if you're using it.

If you couldn't tell by now, movement goes well with Ahri (and useful on pretty much every champion in the game), I pick up Swiftness for that reason. Ahri has a low base move speed (305), and with this mastery and starting with boots; makes her quite fast for early game.

As mentioned earlier, if played/built well, Ahri does not have mana issues. Thus no need for mana regen masteries. I pick up Runic Affinity as my last mastery. While you're obviously not jungling with Ahri, this makes buffs your steal and buffs your jungle gives you (which in most cases, he/she should be) last even longer. Blue buff allows Ahri to spam her abilities on CD w/o risking running oom - as well as that nice cd reduction to allow you to dish out lots of damage fast and escape with your life!

Follow my build (which is pretty standard tbh), and you should not have much of a problem dominating your lane and ultimately the game (assuming your teammates can back you up).

Start with Boots 2 Health Potion and 1 Mana Potion. This, along with Swiftness , help negate Ahri's problem of slow base movement. The pots, along with your passive, should allow you to stay in lane until you have farmed enough for your Catalyst of the Protector, all while killing your lane opponent (or at least making them back).

On your first back, grab your Catalyst of the Protector, maybe a couple pots/wards and get back to farming/destroying people. Grab your Rod of Ages ASAP, followed by Sorcerer's Shoes.

After this I usually snag Rabadon's Deathcap to utterly destroy enemies and farm like a mad-man. From here on it's all situational.

I typically get Rylai's Crystal Scepter next, boosting my survivability, utility (slows!), and AP quite a bit.

Void Staff is next up if the enemy has started to stack MR to try to counter you as your snowball out of control. If you are having problems at this point somehow, it may be a good time to get some defensive items to counter the enemy team, such as Banshee's Veil or add more utility to yourself by providing spell vamp to you and your team with Will of the Ancients (good if you have a couple of AP's on your team).

Finish up your build with a Deathfire Grasp. At this point you should be pretty much out of control in terms of damage, and with such high AP, the deathfire grasp's use will absolutely decimate enemy champs (around 50% of HP in an instant-cast? yes please). Not to mention the Cool-down Reduction and mana-regen.

Other items:
Mejai's Soulstealer is a phenomenal item if you are constantly getting kills/assists without dying. I typically do not use this because it's a risky item, not to mention I find I'm targeted a lot sooner if I have stacks of Mejai's (I don't like to get too cocky). But if you can pull it off, you will snowball even faster.

Abyssal Mask gives survivability and damage! If you are getting smoked from an enemy AP - but want to keep your damage up, grab this in place of void staff.

Mercury's Treads: Again, if you're finding yourself in a sticky situations a lot, or the enemy team has heavy CC - it is definitely worth grabbing these boots, especially after you have a void staff.

I tend to grab Elixir of Brilliance anytime I'm high on gold, but still slightly short of for the next item I'm grabbing. AP and CD reduction... obviously buy when you can capitalize on it, and always have them on after you complete your build.

Vision Ward/ Sight Ward: Ward, ward, ward. Wards can make the difference between winning and losing, and not warding is one of the most common mistakes people make. It is NOT only for supports/junglers, everyone should contribute. Ward dragon, ward baron after level 11-12, if u're constantly pushing past mid, ward to protect yourself from ganks. Ward their jungle while your team is there so you're not blind the next time you go in. Same goes for your jungle if the enemy is often in it.

To repeat, Ahri is a high-mobility assassin mage. This means she's squishy (especially before Rod of Ages). She is also highly reliant on landing skill shots.

Ahri definitely takes some practice to get good with. The reason I love Ahri is because she can destroy people if played to her potential, but she has a high skill-cap.

Knowing how to approach each combat situation will ultimately take practice playing her. So, Summoner, keep at it!

Some basic tips however:
(Passive) Soul Eater used properly can save your life in fights. Knowing when to hit as many targets as possible to heal and when to hit that main target can be a tricky split-second decision.

(Q) Orb of Deception is her main nuke, and a skill-shot. it hits like a truck if you can hit them on the way in and out... and doesn't diminish in damage or anything the more champs it hits. In essences, hit as many enemy champs as often as you can with this. Don't miss! especially with your passive up.

(W) Fox-Fire Just adds more damage (prioritizing champs)! Who can argue with that. Pop it when you are close to targets you want to nuke.

(E) Charm is another skill-shot. This has immense utility and damage all wrapped in one! I find charm to be the most devastating ability Ahri has. Use this ability to open fights when the enemy is out of place. When you are in the opportune position yourself, disrupt their main damage (usually the carry) with this ability, followed up by an Orb of Deception and other damage to try to destroy the enemy while they can't even retaliate! Use this ability to save your life if someone happens to get their hands on you. Whatever you do, DO NOT waste this ability. This ability is what wraps Ahri into an unstoppable force. Not all may be lost if you botch it up once - as it's a fairly short cool-down - but do not make it a habit!

(R) Spirit Rush is Ahri's aforementioned high-mobility. This ability will save you, destroy the enemy team, and chase down those cowards! Knowing when to use this is also important, maybe more-so than Charm due to the longer CD. This is essentially a triple flash with damage, so use it to skirt the fight while dealing damage, get away from those nasty champs who wish to touch you, and finish off that ace for your team. This will also help you maintain or fix (destroy if you do not use correctly) your positioning for team fights. Use it wisely!

Blue buff is far from a necessity for Ahri, however, lowering her already short CD's even more can't hurt. Having blue buff + Elixir of Brilliance + Deathfire Grasp essentially gets your CDR capped. This allows your to throw out ridiculous amounts of damage and you will almost certainly have your Spirit Rush and Charm up when needed.

If a picture is worth a million words, videos are probably priceless. If you have LoL Recorder (if you don't, you probably should)
Here is a link to a video of me as Ahri in middle lane vs. Morgana:
Replay of an Ahri Mid.

The game was only a normal, and in no way am I pushing that I am amazing at this game (even in the replay you can pick out dozens of things I could've done better). I do feel it does a good job at showing how Ahri can be played, however.

Pros:
+ Easy to farm with
+ Mage without much of a mana problem
+ Can deal true damage
+ Even with low AP ratios, hits like a truck if played correctly
+ Can carry your team pretty hard if necessary
+ High mobility = High K/D ratio and gives you an ace in the hole if you mess up
+ Very rewarding for high-level play
+ Ridiculously fun to play

Cons:
- Low base move-speed
- Squishy
- Punishing if you miss your abilities
- No targeting abilities
- Typical mage threats, such as silence/getting cc'd before you get in a good position

In summary, Ahri is an extremely fun champion to play. She has a high skill-cap but is very rewarding. Like most champions that have been released lately, she may be a bit over-tuned, but I'm not too worried about that, since only good players will be able to take advantage of it - thus an Ahri in low-elo most likely won't destroy a game to the point of being no fun.

Practice makes perfect, as the saying goes. Keep playing with Ahri and I don't doubt you will find her fun and rewarding. All in all, I believe Ahri is a great addition to the league and I am looking forward to playing her more.

I will constantly keep updating this guide, as she is a new champion. There is bound to be changes to her or finding even better ways to use her. I will also continue to add replays when I have more time to play as well as any information I find helpful. Enjoy!