Recommended Summoner Spells
These summoner spells should be your common picks because I think that they fit Ahri best. This is just my opinion and thus I also have a list of viable summoner spells that I will also explain to you after I explain to you what the recommended summoner spells are and why they should be common picks.
sp Exhaust: This spell will save peoples lives and win ganks. It may save you or it may save a teammate but it really comes in handy. It lowers damage output and Movement speed, which helps you to solo an enemy, or keep your team safe during a teamfight. It will also give some good CC during ganks. The fact that this ability can only target one enemy and only allows you to neutralize a target for 2 seconds is quite useful In a 1v1 situation. Normally you should only enter if the enemy is around 50% but if you have Exhaust you can go in if theyre about 65%. With little sustained CC Charm having something to follow charm up with can prove very useful. sp
sp Ignite: This is a great addition to early game burst damage. Any time an enemy is able to escape your range is not safe yet. Not to mention early game mana may be more of an issue than expected and when it comes to finishing a chase kill, sometimes, whether due to mobility or simply going OOM. Also adds to burst damage overall and will also give the psychological advantage of fear. If an enemy sees their health depleting while flashing red from the ignite it is much more difficult to decide to attack an opponent. This works in your favor because despite Ahri's insane burst damage, if the enemy turned to attack you before they died, they could deal a fair amount of damage. Ignite is a spell that is situational and should always be taken against a healing team. Generally though its personal preference and can be switched or Exhaust or Flash.
Viable Summoner Spells
This is a list of summoner spells which I find viable on Ahri, however I do not find myself using them very often.
sp Ghost: This is a very useful spell on really any champ in general. What is good about using it on Ahri you can catch any enemy and CC/Finish them off for your team. Also can be used to escape sketchy situations after your ultimate is on CD. No cons here really, honestly I have no preference in terms of a utility summoner spell. sp
sp Flash: This spell is great for ganking and escaping. Good summoner. Once Spirit Rush is on CD Ahri has no real escape mechs. Ghost will help you outrun enemies but you are still vulnerable while in thier range. Flash will allow you make a complete escape by going through a wall. It can also be used to pull off successful early game turret dives. The problem here is the CD. It is perhaps the longest of all summoner spells or at least feels like it with also very little uses on Ahri. When iniating it adds no bonus, when DPS'ing it add no bonus, only in escape will it be helpful. sp
sp Cleanse: Good summoner as CC usually means death in a ranked game. Docent see much use because of its lack of utility but I would recommend dropping an aggressive summoner spell in most situations if you can tell the enemy team is composed of hard CC champions like Sion. They spell certain death for Ahri. sp
I take 21 points inoffence and 9 in defence for a few important reasons.
The early game damage from offensive masteries and 6% bonus on low health targets is very good on Ahri. Not only does Mental Force and Blast give AP to Ahri's four ratios (one on each ability) you will gain the ability (or perk) Executioner. This is crucial to Ahri due to the nature of her playstyle. Considering most of your kills will be carried out on targets below 50% HP the 6% bonus damage on targets below 30% will be very helpful. As a personal preference I take Exhaust and Ignite to help me take early game lane control and secure kills. As such Summoner's Wrath gives me the greatest returns for a skill point. Havoc is more of a transition perk to allow us access to the higher level masteries available. As an AP assasin you cannot really go wrong with 21 points in the offence tree.
To those who are partial to utility, consider the fact that the spell vamp and mobility will mean nothing without the offensive power to back them up. Hardiness gives strong early game survivability against minion aggro and enemy auto attacks, whether they are Lux or Tryndamere. Resistance Offers more of a late game advantage against AP carries who will try to stop you from casting spells by killing you before you can click. Personally I find Vigor a nececitty in the lane. Especailly when I start with 3 pots, my constant health regen discourages the opponents harass and allows me to continue staying in range of my opponent without getting forced out of lane.