This is my 1st build, and it's a Ahri Builddddd. So you may have seen my build, and thought, "WTF?" but yea, keep reading, you'll understand why in each little sections.

*NOTE- THERE WILL BE NO IMAGES LOL

*NOTE- Some things from this build may be helpful so take whatever you can from it :D

*NOTE- Please suggest anything, I will update this so it will become a perfect build.

Pros

Can intimidate enemy if used correctly
Carry's the game
Good Farmer
Good skills
Good Ganking Skills
Sexy ;D

Cons

Squishy
Really Slow
Helpless when Ganked
Usually gets targeted the most when solo mid
Doesn't have really good skins D:

I don't specifically care about runes, it's just remember that Ahri is a AP champ, not a AD, so make sure to get something related to AP/Mana/Mana Regen/etc. Also, I make Ahri a bit tanky so she might be able to live through ganks late-game.

This is just how I set it up, you don't have to follow it, it's just I play better w/ these masteries. You can change it up to a way you want it too.

Morello's Evil Tome
Fiendish Codex (1275) + Blasting Wand (860) + Recipe (215) = 2350
+75 ability power
+12 mana regeneration per 5
UNIQUE Passive: 20% cooldown reduction

Deathfire Grasp
Kage's Lucky Pick (765) + Fiendish Codex (1275) + Recipe (600) = 2610
+60 Ability Power
+10 Mana Regen per 5 Sec
UNIQUE Passive: 15% cooldown reduction
UNIQUE Active: Deals magic damage to target champion equal to 30% of their current health (+3.5% per 100 Ability Power) with a miminum of 200 damage. 1 minute cooldown.

Well... This will be a really LONG explanation so please bear with me. (Full of Calculations)
So you see, Morello has +15 AP, +2 Mana Regeneration per 5 Sec and the passve is +5% more CDR. Against that, Deathfire Grasp has -15AP, -2 Mana Regeneration per 5 sec and and this passive is -5% CDR. Just by looking at this, Morello is a much better choice, but Deathfire has another UNIQUE passive, which is "Deals magic damage to target champion equal to 30% of their current health (+3.5% per 100 Ability Power) with a miminum of 200 damage. 1 minute cooldown." So you think... ummm, I don't want to calculate, so I'll do it for you..

DEATHFIRE GRASP CALCULATIONS
________________________________________________________________________________________

so the 1st part, "Deals Magic Damage to target champion equal to 30% of their current health"
So suppose you fighting another Ahri Lv18 the same build except with a morello, so that means the Ahri has 3690 Health, 3690x30%= 1107 dmg.

Now the second part"(+3.5% per 100 Ability Power)"
So you have approx. 395AP,let's round it down to 300AP to make it easier, so it will be 3.5%x3=10.5%, now let's get 10.5% of Ahri's full health 3690 3690x%=387.45 dmg

Now add up the damage done so 1107+387.45=1574.55 magic damage done.
3690-1494.45=2066 Health Left, pretty worth it? i think so, not only that, that's extra damage,
so use your Q which is 280(+66% of AP) now let's calculate your 66% of AP
395x66%=260.7+280=540.7
and supposing u spam all your skills and now let's calculate your W (we will do two calculations of this because the 1st one does less damage then the other 2)
the W does 160(+38% of AP) so 395x38%=150.1+160=310.1 and your additional two firefoxes does 50% of 320(+75% AP) so first 395x75%=296.25x50%=148.125x2(2 additional firefox)=296.25
Now your E skill Charm
180(+35% AP) 395x35%=138.25+180=318.25
Now your R skill
180(+30% AP) 395x30%=118.5+180=298.5

Yes, it's done now, so the easiest part, add them up
Deathfire Grasp 1574.55
(Q) + 540.7
(W) + 310.1
(W) + 296.25
(E) + 318.25
(R) + 298.5
___________________________
3338.35 DAMAGE

MORELLO'S EVIL TOME CALCULATIONS
_________________________________________________________________________________________

Now in this, guess what? None of the Deathfire Grasp Calculation, Only skill calculations

So, Ahri has 410 AP with Morello's,
Your Q skill will do
280(+66% AP)
410x66%=270.6+280= 550.6
Your W skill will do
1st Part
160(+38% AP)
410X38%=155.8+160= 315.8
2nd Part (2 additional firefoxes
50% 320(+75% AP)
410x75%=307.5+320=627.5x50%=313.75x2=627.5
Your E skill will do
180(+35% AP)
410x35%=143+180=323.5
Your R skill will do
180(+30% AP)
410x30%=123+180=303

(Q) 550.6
(W) +315.8
(W) +627.5
(E) +323.5
(R) +303
__________________________
2120.4 DAMAGE

Which is worth it? I don't know, you can choose, because these calculations aren't accurate, so don't expect your spams to do 3338.35 DAMAGE, it maybe somewhat close but, don't count on it. I would get Deathfire but you can get Morello's, and I have changed my build from Morello's to Deathfire.

*NOTE-I am considering this because my friend suggested me to stop using Morello's and get Deathfire Grasp since it will give me better burst.

1st-Doran's Ring
Now the reason I pick this is obvious, gives you extra 100 health, I can't count how many times I ran away from a gank early game w/ 100 HP left. Also gives you a 15AP allowing you to give a little burst in your Q. The 5 mana regen, for you noobies, use this effect wisely, when your outta mana, stop going back to your base and back to your lane, just attack minions w/ regular attack and wait for you mana to regenerate. *PS- keep away from champs during this process

2nd-Boots of Speed
This is just the obvious, easier chase and run away

3rd-Catalyst the Protector
This is just for more HP and Mana, also, once you get this, FOCUS FOCUS FOCUS PLEASE FOCUS on last hitting minions, upon leveling it restores your health and mana!

4th-Rod of Ages
This is just a better version of the Catalyst the Protector, it gives a little bit more HP and Mana, also +60AP, this is a lot, also read the passive yourself, it's self-explanatory..LOL

5th-Sorcerer's Shoes
Little bit more chasing and run away speed, and +20 magic penetration, this may seem like a little bit but it's still worth it guys.

6th-Fiendish Codex
It is just to build up to Whichever you like, the Deathfire Grasp, or the Morello's Evil Tome

7th-Deathfire Grasp
Explained in Chapter ABOVE

8th-Needlessly Large Rod
SELF-EXPLANATORY- much more high burst...

9th-Rabadon's Deathcap
140AP=HIGH BURST and the unique passive takes the overall of your AP and adds another 30% of it which leads to...HIGHER BURSTTTT


*P.S- at this point, once you have 435 gold, sell your Doran's Ring and buy the regrowth pendant.

10th-Regrowth Pendant
simple health regen...

11th-Warmog's Armor
get around 3k gold and buy the Warmog's Armor
*THIS IS LIKE THE WHOLE MEANING OF MY BUILD AND I WILL STRESS OVER THIS
This helps Ahri to grow tanky, b/c as far as I've been playing as Ahri, she is squishy even late-game, I can die in a second when I'm ganked. Also the reason why warmog is amazing is because Ahri is a amazing farmer with her Q. The warmog's effect is +920 Health and +30 Health Regeneration, this can make Ahri's full health over a 3000. The passive is +3.5 health and +0.1 health regen per minion kill, meaning late-game, farm with your Q on a wave of 6 minions and the calculation is 3.5x6= 21, so just killing one wave can get you +21 health, kill 5 waves of minions and you can get +105 health. That's pretty nice if you're having a hard game, when you're getting ganked a lot. Also, Ahri is perfect 1v1 throughout the game on most champs, and the other passive is +35 health and +1 health regeneration for each champion kill or assist and is capped at 10 stacks. Thus, Ahri can be a AP/Tank for the team, which can be pretty kewl.

12th-Rylai's Crystal Scepter
This is basically for crowd control, gives slows and etc, nothing to explain much for it.

Early-Game
Don't expect to get a whole lot of kills before you even get your ult, "Spirit Rush" Before you get your ult, just keep farming minions while avoiding champ attacks. When you farm, use your Q, but not to aggressively, and also, try to hit the champ little by little. When you keep attacking the champ and farming the minions until Lv6, once your level 6, stop using skills, keep attacking minions with regular attacks. Keep doing that until you get a decent amount of mana.
Start off by aiming Q at the champ, they will either run or not move.
Next, use your R to position yourself where you can use your E without having any minions to bother you and use your E.
Now that your enemy champ is running towards you, use your W so that the fire fox comes out. And b/c the fire fox delays, use your Q, which should be ready by now after the cooldown while your emit your Orb, your fire foxes will emit at the same time giving high burst. After this, it should be enough to get the kill, if not, chase.

*NOTE- THIS IS THE WHOLE PROCESS Q -> R -> E -> W -> Q AND THE ONCES IN BOLD SHOULD BE DONE IN A QUICK PROCESS, OR IT WON'T WORK WELL.
ALSO, IN A EARLY GAME, MIA CALLS ARE NECESSARY, BECAUSE THE MID WILL BE ON A HIGHER LEVEL THAN OTHERS

Mid-Game
Around here, the process of ganking should start on YOU they should try to gank you around there. If not, you will keep on soloing mid, you should have at least 3 kills by Lv10, and you should gank, since you should be on a higher level than the others.

*NOTE- AN IMPORTANT THING HERE IS, MAKE SURE YOUR TEAM CALLS FOR MIA "MISSING IN ACTION" THIS CAN HELP YOU FROM AVOIDING GANKS, AND LETTING OTHERS AVOID GANKS. (ONCE A MIA IS CALLED, TRY TO GET NEAR THE CLOSEST TURRET, OR EVEN HIDE, DON'T FIGHT THEM UNLESS YOU ARE FULL HEALTH AND THEY'RE NEARLY DEAD)

Late-Game
You should be full of burst by now, ganking and helping other lanes. Make sure you call on to gank champions, so that they know to position the enemy champion, meaning near a turret. Also, you ARE a carry, so you should start using teleport to start some ganks and etc. Nothing much to state here, just stick with at least 1 champion, because the other team will be moving in a crowd through the jungle or moving solo.

*NOTE- OHHH YESS, NOT TO FORGET, DON'T START ATTACKING TURRETS ALONE, MAKE SURE YOU START ATTACKING TURRETS WITH OTHER CHAMPS, BECAUSE THE MORE FURTHER IN YOU GET, THE MORE YOU GET IN THE ENEMY BASE

Early-Game
Now this is a much easier process than Solo Mid, because you have someone to rely on. Just start using your Q not to aggressively but just enough to keep damaging the same champion. Make sure to hit the most squishy champ, this allows you to feed on them, if not, hit the most tanky, then the squishy. Tanks can get annoying late-game, squishys are easy to kill w/ games even in late games. You can use the same skill sequence Q -> R -> E -> W -> Q with the exact same speed. Make sure when you do this, your partner is attacking that champ too, or keeping the other champ distracted.

*NOTE- YOU DON'T HAVE TO GET KILLS HERE, JUST MAKE SURE YOUR FED, OR YOUR LANING PARTNER IS FED. FEEDING ON THE OTHER CHAMP CAN MAKE A BIG DIFFERENCE.

Mid-Game
Important thing here is again, MIA calls, you don't want your mid to be underleveled because of deaths due to ganks. Also you want to avoid feeding the other team since your really squishy. You can avoid that by actually giving MIA calls.

*NOTE- DON'T FEED, GET FED. ALSO GIVE MIA CALLS, NOT IN YOUR HEART. EVEN IF YOU THINK THEY'RE BACK IN THEIR BASE HEALING, JUST GIVE THE CALL, IT'S WORTH IT

Late-Game
Even though you will be underleveled then the mid champ, you can still effectively carry the game, start roaming around the jungle to start some ganks. You can kill neutrals on the way, especially the blue buff, it can get useful.

*NOTE- GANKING WITH THE CHAMP THAT DID THE SOLO MID CAN MAKE THE GANKING MORE EFFECTIVE, OR I SHOULD SAY, A MORE ASSURING KILL.

Ahh yes, summoner spells, why I chose Teleport and Flash...no specific reason, it's just easier for chasing and ganking.

I WILL EXPLAIN THE SUMMONER SPELLS CONSIDERING AHRI

Exhaust- This can help you for chasing champs that you couldn't kill throughout the whole game. After using your R -> E -> W -> Q sequence and the champ didn't die and their running away, this is perfect, give time for your skills to be done with the CD.

Ghost- This is just a replacement of my flash... haha

Heal- It'll be good if your not good at avoiding champion attacks, and you're always near dead, use the heal to help you keep laning without using B

Revive- This... is just Shi.T

Smite- I don't think ahri isn't made for jungle so... This... is just Shi.T

Surge- Not that useful for Ahri, but it's still good when your ganking a champ, not recommended though...

Cleanse- To me, I find this skill just for running away, which can be good since Ahri does get ganked a lot, also many stuns on her.

Clarity- This can be necessary for people who play Ahri really aggresively, but, it's not required if you know how to limit her spell usage.

Ignite- This is good if your not good at estimating how much Ahri's spells can do, so suppose you use the R -> E -> W -> Q sequence, they live, you use exhaust and they still live w/ like 5hp, this is useful for that timing, but it won't happen if you know how much Ahri's can damage.

Promote- umm... sure, you can but it won't benefit Ahri at all, if just benefits the minions lifespan....

Clairvoyance- this is.... not good, not bad, it can help when MIA calls are given and you want to find out if a champion is heading towards you but... I just highly suggest you go to your nearest turret once a call is given..

AHRI IS A SLOW CHAMP, SO RUNNING AWAY IS HARD, AND I CAN'T STRESS HOW MUCH ON PEOPLE NEED TO CALL ON MIA... PLEASE... CALL MIA, THIS IS PART OF TEAM WORK LOLOLOLOLOL......

ALSO, MAKE SURE YOU ASK IF THEY NEED GANKS, IT CAN HELP FOR THE LANE TO PUSH.

WELL TEAMWORK IS WHATEVER YOU THINK IT IS, SO JUST DISCUSS WITH YOUR TEAMMATES

So maybe if you read through my whole build so far, you saw the quote, "Can intimidate enemy if used correctly" but how? well, I'll explain to you well, gonna try without a picture so bear with me...

Your Q is a hard skill to master, but this is the skill used for intimidating/backing off the enemy champion....

Here's the way, people use this like Sivir boomerang, it hits through the champ and it hit the champ again on the way back. This does decent damage but it doesn't make the enemy champ feel like they've been damaged badly. My way allows your Q act like a burst, damaging the enemy champ badly thinking o ****, their ahri is glitched.

Click your Q, once the arrow thing comes out, hit the enemy champ at the tip, if this is done well, it will look like u have a burst skill, and a skill that allows a 2 way damage.

This is the base of my skill, hitting enemies at the tip is the base

*USE YOUR Q AND HIT THE ENEMY CHAMP WITH THE TIP.

sorry if i suck at explaining, if you don't get it, comment and i'll contact you

Q, Q, Q, Q....
EarlyGame
last hit last hit last hit.... if not, wait until most minions are nearly dead, then use your Q

MidGame
Same as earlygame, you have a decent amount of damage but not enough to kill minions with one Q

Late Game
You will have your Q to have good damage... so you can farm with only your Q, but use a bit of minions dmg