At start i want to say few words about mid gameplay to you.
So, never forgot when u push do not paly agresive. When u waste all cds to your opponent under his tower ull have just a little chance to escape from jungler if he comes.
Also do not let your opponent push u, u can allways use q to creep when u play ahri so do not let hem push to your tower, u can creep under your tower but ull allways miss some creeps and i realy hate when i miss my farm .:)
If opponent junglers camping on mid u have to buy some wards it will help u much.

Ahri has two skill shots. When u want to play her it would be good to learn skill shots.
U can deal quite good dmg with foxfire and your ultimate but when u hit charm (e) then orb of deception (q) + foxfire and ultimate (w,r) you do much more dmg.

Best wain how to haras with q is when you get some creaps + hit your opponent, its realt easy to creap with q so u can to it but remember, allways whn ull creap + harras with q you will push the line (Sometimes its realy good vs. pushers like morgy or malza... :) )

U have to start with boots and pots cose ull get some sustain and mobility.
Then i like to buy 3x dorans ring. After dorans rings i go for will of the ancients and rabbadon after rabbadon i buy rylai s crystal scepter after scepter i build road of ages or i go for zonya if i need it (overfocus :S) or void staff or u can abyssal scapter.. but its about situatiom.. when i dont need some special items cose of bad situation i go for road of ages.

As a last item u can buy Guardians angel or banshee or any deffensive items u need in game.

When u can hit your e do it if its possible, the hit your q and start foxfire. Its realy amazzing burst and when u hit opponent on lvl 6 with this combo hell not suvive probably (after second e,q,w u have to cast your ulti then next q then 2 charges of ulti + ignite if u need. (This is sequence to single target)

Skill sequence to more targets is litle similar with sequence to one target u just have to hit ad carry or ap carry with your e if its possible + hit more targets then one with your q

I like to pick Ignite + flash (standart summoner spells for caster)
But u can pick ignite + exhaust or ignite + cleanse. (Ahris ultimate gives u perfect mobility so if you will play safely you will not need flash, but remember that u need dmg from your ultimate too)
U can also pick ignite + ghost but i realy hate games with mages when i dont have flash ;)

I like to take yellow runes to mana regen because this mana regen runes works perfectly with your passive (i mean u can cast a lots of spells and your mana will return back after few momentMy red runes are to magic penetration and my blue set is 6x ability power and 3x magic penetration
My quint esences are to ability power
U can take Quint esences to magic pene too but then take all blue to ability power

Other rune build is: Yellow - mana regen, blue - magic resist, red - magic penetration and quint esence - ability power