PROS

+ Good waveclear
+ Strong 1v1 potencial
+ Mobility for ultimate
+ Ideal for roaming and getting picks

CONS

- Long cd on her R makes her vulnerable to ganks
- Without her R she has no kill pressure
- Has a lot of counters
- Weak early game

Flash

Standard choice for Ahri. She is a very immobile champ with only mobility her ult which has a long cooldown. So having another option for engage and disengage is crucial. She can also perform combos like Flash + E Charm to catch people off guard or even Flash + Q Orb of Deception.

Ignite

Ahri's nature makes Ignite pretty much mandatory. Her damage isn't that great and she needs Ignite to secure kills, or finish off targets in duels. Also she depends a lot on roaming to snowball. She loves roaming bot because there are 2 kills instead of one and the champions there are usually squishier than top lane. Thus, Ignite also counters the Heal that the enemy will be running bot.

Cleanse

You want to take Cleanse when the enemy mid + jungler have both CC to be able to break free from the CC and run to avoid them CC chain you and burst you down. It is rare but when it happens, your life can be hell without Cleanse so make sure you pay attention and go for it.

Domination

Electrocute

It is the best keystone for Ahri since it gives her the extra damage she needs to win trades or secure kills. Also it is very easy for her to land unlike Arcane Comet or collecting Dark Harvest stacks. Easy to proc burst in lane that gets you to snowball into mid game.

Taste of Blood, Sudden Impact, Cheap Shot are all viable options. Choose according to the enemy team. Cheap Shot for True damage after Charm usually when facing tanky enemy teams to deal the extra damage after E Charm. Sudden Impact for squishy teams for the extra damage after using R Spirit Rush and Taste of Blood for hard matchups for the healing because Ahri's early game is kinda bad and she needs the sustain.

Eyeball Collection

It is your best bet for scaling since Ahri sucks at that. So she really needs the extra 30 AP when fully stacked to snowball and be able to close out the game before she falls off in the late game.

Ultimate Hunter

It is by far the best for Ahri. Yes i know Ravenous Hunter provides massive heals but as Ahri you have healing through your passive and if needed more take Taste of Blood as said before. On the other hand, you are very dependent on your R Spirit Rush and Ultimate Hunter offers the cooldown reduction to use it more often. Without R you are kinda useless unless you are very far ahead, so go for it.

Sorcery

Manaflow Band

It helps Ahri with the extra mana due to the fact that her abilities aren't the cheapest out there. So it is very beneficial rune to be able to cast more spells and stay in lane longer until you get enough gold for your powerspikes. You can also go for Nullifying Orb if you are against hard AP matchups and you need the survivability.

Transcendence

Has been changed and now offers 5 ability haste at level 5, and again at level 8 for a total of 10. But at level 11 on champion takedown, it reduces the remaining cooldown of basic abilities by 20% (reminds of Spear of Shojin), letting you use more often your abilities and thus being more flexible.

Inspiration

Glacial Augment

A rare but good option for Ahri. Works great against enemies with high mobility that will make it hard for you to land your skillshots, or even when your team has low mobility you can also go for Glacial Augment to help them not get kited in teamfights or skirmishes.

Magical Footwear

Free boots to invest the gold towards your powerspikes and be able to snowball harder. They also offer some extra movement speed to add some flexibility to your playstyle.

Minion Dematerializer

This rune is crucial for Ahri to be able to one-shot the backline minions also known as "caster minions" with her Q. Because she runs attack speed instead of damage in the first of the tree minor runes take Minion Dematerializer to use it on caster minions and deal more damage to them and thus one-shot them with two Qs early. If you dont do that they will survive with a tiny bit of health wasting, mana, time and of course risking not to get them.

Cosmic Insight

Some ability haste for your summoner spells and abilities. It is very helpful because it increases your chances of surviving by letting use more abilities and as a result, more passive healing, more charms, which is your only peel speel, and more Rs Spirit Rush, which means more mobility.

Essence Theft is Ahri's passive. Whenever she hits an enemy with one of her abilities, she gains a charge of Essence Theft. She can gain up to 3 charges per ability cast. Once she reaches 9 charges, her orb changes color from blue to green, signalling that the next spell she uses heals her based on level, Ability Power, and enemies hit.
when getting low you can easily use Fox-Fire to bring yourself up to 9 charges and then using Orb of Deception across a huge minion wave will return you a respectable amount of health in laning, and later on in the game with lots of AP it can provide massive heals (like or even better than Ravenous Hunter).

Orb of Deception is everything for Ahri. It provides great wave-clear and main damage source in one spell. Learning the range of this ability is crucial because it hits twice, you want to be trying to hit enemies in lane at the very edge of its range so they can't dodge either side of it. Also you can one-shot the castor minions when this spell is maxed at level 9, assuming you're not terribly behind. Pro tip: try to combine Flash directly after casting Orb of Deception. That will hide the animation of your Q and get a sneaky kill on someone, same as how the Charm + Flash trick is performed.

Fox-Fire's only tip is that each flame targets independently of others, meaning each flame has its own range and it does not cover the whole range that is affected by W.
For example, when Ahri finds herself surrounded, if she hasn't Charmed or auto-attack an enemy to attract Fox-Fire's flames, every bolt will be flying off on different targets inside their range.

Remember that when using Charm on an enemy only Ahri's abilities will gain increased damage to the Charmed target. Which means that it does not increase Ignite's or Luden's Tempest's damage. A common mechanick with Charm is the Charm + Flash combo. You cast E then Flash afterwards. This way you almost hide the animation completely and catch people off guard.

Spirit Rush Can be used to dodge skillshots, cross terrain, making sure your return Orb of Deception hits the target by relocating its route, and so much more. One important thing to note is when executing Spirit Rush + Flash to cross a large distance, always Flash first and then use Spirit Rush to get full range and make the orbs of your R land. Remember every Ahri's orb whether it is from Fox-Fire or Spirit Rush miss their target it the enemy is out of vision, so keep that in mind.