*UPDATE - Ahri's reworked W has undoubtedly put more favour into this build and I've found good success even when maxing W early on both the hybrid and full AD variant.

First off I'm sure this build will seem extremely skeptical and be flamed upon without more than a glance, criticism is welcome but please read the pros as well as the cons.

To answer this question I think it is important to break down Ahri's kit.
Her Q is capable of harassing multiple enemy champions at once, including through creeps. This places enemies in a vulnerable position where they are constantly open to harass when trying to cs, or must dodge away from the creepwave and into your support's harass/CC. This should of course be used with moderation in order to control creep wave position, but is also an excellent tool in pushing for deep wards, dragon or roaming.

Ahri's W is essentially free trade damage when an enemy is within aa range or has been charmed (fox fire will prioritise charmed champions, followed by the last attacked unit). It also has slightly more range than your auto and fires in series, making it a useful tool for proccing dark harvest.

Ahri's E is a 1.4-2s charm that provides valuable cc and positions the enemy towards your creepwave, support, jg, or tower during dives. Beware that this skill does have a noticeable channel time. This ability can also be flash cancelled and will project from Ahri's new location while aiming towards the original target location with an altered angle and maximum distance.

Ahri's ultimate consists of three dashes with a short (1s) static cooldown between each use, each of which fire three bolts to three nearby enemies. This tool is insanely powerful, allowing for great mobility to initiate, chase, escape or kite mid team fight -all the while applying some heavy damage to multiple enemies. The dash may pass through enemies as well as terrain, and may be held onto for up to 10s after the initial cast.

Ahri's passive is often forgotten, but it is a very useful burst of movespeed every 9s with little requirement. When being chased it may be triggered by a single W press, or used to help catch up with escaping enemies.

In this meta, ADCs are generally weak for a generous portion of the early game in which APCs such as Ahri can capitalise and snowball. This further delays the enemy ADCs items and point of relevance in the game, as well as granting Ahri her own lead towards the late game. It is important to note that even if your team fails to close out the game early, Ahri's burst is easily capable of killing off any non tanks and relatively safe to perform due to her ultimate's mobility.

Ahri boasts a respectable base manapool of 420 at lvl 1, 516 at lvl 6, and 637 at lvl 11. Early tear of the goddess provides essentially infinite mana during the laning stage of the game, increasing Ahri's total mana by more than 50%, and increasing the more it is used. Ahri's W has a base mana cost of 40 with 10% refunded + 4 max per use of tear, making it free to use in lane as much as you want, on top of spamming Q and W for harass, self-sustain and push. You will want to be using your W and E as much as possible when outside of lane too, with some cautious use of Q as well. (Remember you will not lose your Q passive unless you hit at least one unit, you can also build this on camps on the way out of base, though I would suggest leaving it a little below max stacks so the first use of Q can be used for harass without wasting the sustain.) Most importantly, this item provides all this as well as building into your manamune and eventual muramana.

You should aim to grab your manamune as soon as possible. This should be done no later than your second back, and is sometimes even possible on your first. If you find your lane is pressured early you may also delay building manamune til after your hextech GLP (whenever the tear is ready thereafter), as this will be more relevant when behind. On this note you may choose to rush your hextech GLP irregardless of how well you're doing if you think the additional burst and slow will secure more kills. You should expect to finish your muramana around the 18 minute mark, ideally before laning has ended. Keep in mind that your adaptive damage from runes and sub runes may switch to AD when you have obtained your manamune, however this will swap back as you gain more AP from building towards your hextech GLP.

Muramana
For the cost of 2400g you have now obtained an item that has given you a seemingly endless manapool (You should total around 2300 at lvl 11 with presence of mind, hextech GLP and muramune itself, not including the 15% refund, and 20% of max on takedown). Muramune grants 2% of your max mana as AD (+46) on top of the 35 it gives for a total of 81 AD. It also uses 3% (before refund) to deal 6% current mana as bonus physical damage (+144 with slight diminish, assuming full mana at start of a fight). Congrats, your autos now hit for an extra 225 physical on champions from a 2400g item. That's cool and all but the real fun is that single-target abilities also apply the 6% of current mana as bonus physical damage! Ahri's foxfire fires three projectiles, normally diminishing in damage due to the nature of the skill, but now it will apply shock three times in a single cast for around +400 physical damage, with another 140 to your E (sadly this does not apply to your ultimate bolts which I'm unsure as to why, not that it's needed). Your newly beloved has now added almost 700 damage to your burst, with your lowest cooldown and effortless targeting skill now packing an actual punch instead of just burning hairs. Oh, and this will increase even more upon grabbing yourself a luden's echo and/or iceborn gauntlet/lich bane if you're feeling extra cheeky. You are even more difficult to mitigate (especially for the ADC/mid) as your damage outcome is roughly 50% magic, 30% phys and 20% true. If you're willing to try the build out, have fun and enjoy yourself, I recommend a solid duo partner to avoid tilt but I've played this comfortably solo too.

Cons
- I'm a fairly new player to league and only gold so take it with lots of salt.
- Your power spike is arguably delayed until the 18 min mark, but it is drastically stronger.
- Try to coordinate and not run a full AP comp, as with any game.
- Your team may tilt and ping your item a lot until they see you burst down the enemy team.
- Guide is still in development, shall be adding to it and working on alternate and optimal build routes.

TL;DR Your W now do the thicc proc damage instead of kitten poke.