This build guide for Ahri is for mid lane. Ahri is a great AP assassin with moderate burst and very high mobility with her ultimate.

Pros
-Built in sustain
-High burst damage, as well as sustained damage
-Very high mobility with ultimate, great escape as well
-Has one of the strongest CC in the game, Charm (E)
-Low Cooldowns

Cons
-Squishy
-Dependent on hitting skillshots
-Dependent on having ultimate to be effective
-Relatively weak in early laning phase
-Has to land her Charm to get the most damage out of her skills

-Ahri's Essence Theft grants her more spell vamp than Morgana's Soul Siphon even at max power, but is less consistently available. This gives her high sustain but is subject to mana constraints, since she only heals at best every 4 spells, assuming she achieves max stacks with all 3 charging spells. This is helped by most of her spells being potentially multi-target in some way.
-The healing potential granted by Essence Theft is at its best when used with Orb of Deception, as it deals a very decent amount of damage and hits the largest number of targets. The Spell vamp is applied to both the magic damage and the true damage portions of the spell.
-However, against a single target Fox-Fire will return more health, since each of its fires are single-target spells which gain the full effect from Spell vamp.
-If Ahri has Magic Pen Fox-Fire will return more Health than Orb of Deception against minions, provided that Fox-Fire hits three seperate targets and Orb of Deception hits 5 or less minions. Orb of Deception must hit 3 or less targets for Fox-Fire to heal more if its damage is done to a single target. In addition as Ahri's Ability Power increases, this continues to shift in favor of Fox-Fire . This is due to the fact that AoE Spells will proc only 33% of Ahri's Spell Vamp, and since Fox-Fire is treated as three single target spells this limitation applies only to Orb of Deception.
-Ahri's skills get increased damage then attacking a charmed target so landing a charm before using her other skills is essential.

In lane Ahri can be very annoying. Her long range harass is one of the best early and her auto attack animation is pretty smooth as well. Ahri's built in sustian in the form of her passive is so strong that you shold be able to harass almost anyone out of lane if you are properly trading. If you see an opening to auto-attack your lane opponent as he is going in for a CS then do it and immediately back up so you don't take minion aggro. Try to avoid using too many abilities at level 1 because they don't do nearly as much damage as when they get leveled up. Once you hit around level 3 or 4 however, you should be looking to combo all of your abilities. If the lane opponent is outside of the minion wave, then hit them with a Charm and follow up with your Q and W with some autos for some insane harass. Odds are he will be smarter and stay behind him minions wave, in which case you can play aggressively with your Q and push the lane (putting you at risk for a gank) or you can sit back and wait for level 6.

Once you hit level 6, your mentality should be to pick up a kill somewhere. If your lane is too passive and you don't think you can pick up a kill there, then push your wave to the enemy turret and go gank a side lane. If neither side lane is available for ganking, then multiple things can still be done to gain an advantage over the enemy mid laner.

The safest thing to do while your lane is pushed is farm your wraiths. You are at little risk for being ganked since you are on your side of the river and you will gain some extra gold in the process. If you have enough vision and knowledge of where the enemy jungler is, then taking the enemy BIG wraith is a very good way to gain an advantage and deny your enemies of gold.

Another thing you can do is follow your jungler into the enemy jungle to counter jungle or gank. Roaming by yourself is good, but you are susceptible to walking through a ward and getting counter ganked. If you roam with your jungler they may have an oracles to clear out wards or you could find someone and be in a 2v1 situation in your favor.

Another thing that is more advanced but can work very effectively especially if you have been roaming a lot is baiting your opponent into thinking you are roaming. If your lane opponent thinks that you are roaming then he may feel inclined to follow you to that lane for a couter gank. However, if you are to just sit in a bush (MAKE SURE YOU KNOW IT'S NOT WARDED) and wait for the enemy laner to walk by then you can easily land a blind charm on them and burst them down.

Using Blind Charms to Catch People

Ahri's charm can make or break team fights and hitting it is something that great Ahri players will do 99% of the time. Making the obvious charm in front of the team will likely not get you where you need; the enemy will easily evade it if they see it coming. The key is to predict the movement of an enemy champion and use areas on the map that are blind to the enemy team to get a charm in. A great place to do this is right outside of the base tower when you are sieging the tower. If you stand diagonal to the tower and charm over the wall, this could be the initiation your team needs to follow up on a series of chain stuns. Just be careful not to bait your own team into doing this if you know that you will lose a team fight under the tower, even if it's 5v4. Be careful of charming the tank as well; by doing this you may bait your allies into using their spells on the tank, which puts them on cooldown and thus makes your allies more vulnerable to the enemies with higher damage. Be sure to try and charm the AP and AD carries if possible, or otherwise the support.

Team Fighting

Whether you are using the assassin build or the sustained DPS build, your positioning in a teamfight will not change. You are not your team's tank or initiator. There is no reason for you to be leading a charge on the enemy team. Landing a charm is amazing for your team, but it has a long range. You should be able to land a charm and have your entire team follow up on that target without putting yourself into a position to get caught.

You can walk forward and poke with your Q, but make sure to not get caught out as Ahri is relatively squishy and CC will shut her down VERY quickly. Remember that Ahri's Q does TRUE DAMAGE so using this as a poking tool is extremely effective on squishies and tanky champions alike. If by chance a squishy walks out of position even a little bit then try and land the charm on them and take them out as quickly as possible to gain an instant advantage in the ensuing teamfight.

Once a full-scale teamfight breaks out you're going to want to do as much damage as possible, but try to get to the enemy carries if you can. Ahri's AoE damage in a teamfight is remarkable and should not be underestimated. Don't be afraid to dive into the enemy back lines with one or two charges of your ult because you always have that third charge to escape if you need to or to chase down any runners. Remember that Ahri is VERY mobile with her ult but if it is on cooldown in teamfight then you should be very careful about your positioning and try to stay on the outside of the battle.

Initiating and counter-initiating

You can initiate with your ultimate to catch targets out of position. If you see someone clearing a ward or trying to poke around with their face to see what's going on, don't be afraid to use your ultimate to try and catch them. This is your job and due to its short cooldown (as far as ultimates go), your ultimate allows you to take these risks and to catch champions that are out of position. Your team can always hold out and stall the game a bit to wait for your ultimate to come back up. So if you're unsuccessful, make sure you tell your team to wait a min for your ulti to come back up before your team tries to engage again.
When enemy champions are trying to initiate on your team you can peel using your slows (assuming you have Rylais) to really slow down and sometimes stop enemy engages. You also can use your Charm spell (E) to accomplish the same thing. It's a great counter-initiate spell and if you see the enemy team charging in, don't be afraid to step up and use it to save an ally because you can always rely on your ulti to get you out of those bad situations.

Using Ultimate to dodge Skillshots / High Mobility

You can use your ultimate to dodge enemy skillshots. In addition you can use it to harass in lane, especially with the way I like to build Ahri. It has a relatively short cooldown, especially with blue buff, so don't be afraid to use it just to do damage to the enemy (you don't have to save it to kill them). Just remember to play more passive and just harass with Q when it's on cooldown (you'll be targeted by the jungler if they know your ultimate is down). You don't have to play too passively if you still have your flash up (since you'll have that as an escape). See this video below to get an idea on how to use your ultimate to dodge skillshots

When using your passive spell vamp procs try to always hit the maximum amount of creeps to get the most spell vamp back.

Use your ultimate to escape ganks and to avoid threatening skill shots like Ezreal's or Ashe's ultimate.

Your Fox Fire (W) spell counts as single target damage so when combined with Rylai's it will actually slow for the full amount three separate times.

If you Charm and then flash immediately the charm will go to your new flash location and is hard for the enemy to dodge. This is hard to pull off though and could result in your wasting your flash if you miss it.