Ability Power Miss Fortune? Definitely a great choice.
It's all due to preference, whether you play AD or AP Miss Fortune, but I feel AP utilizes more from Miss Fortune than a strong auto-attack, Double Up and Bullet Time. AP not only runs three of her skills, but with a Lich Bane, the item proc stacks on Q. AP Miss Fortune uses her E more than her Q, making it easier to harass without having to line your Q up. AD MF has a great Auto-Attack, but with impure shots, AP MF can still has some damage in her Auto- Attack. If you aren't convinced yet, at least give it a shot, I'm sure it won't be a "Miss Fortune" to play AP style. Be wary this build does need some practice, but gets easier and easier along the way, Like any champion, It's all in the skill.
:D


*Once I learn how, I'll add photos, Because image shack is being a weirdo.

Q:Double Up
Like I said, Q stacks with Lich Bane, So lets say you have 600 AP, You get 165+600 Damage in this skill, and as well as if another enemy takes the second hit, you get 765x115%

W:Impure Shots
What? The AP ratio for Impure shots is 5%?! Yeah, And anything greater is already OP. This skill is underestimated in damage, but truly it is an OP Malady. In this picture I have 732 AP. That gives me 14+34 Magic Damage Per attack, but wait, This can stack at least 4 times, so If I get full stacks on an opponent I get 48x4+Attack Damage, And don't forget the early game Malady that stacks on this as well. Malady also shreds MR, allowing this W to deal more damage.

E:Make it rain
This skill is an early game harass, With MF's movement speed and impure shots, you are surely going to deal some nice damage. You can farm off of minions with one cast, And it stacks with Rylai's so it has more slows to set up your Ultimate.

R:Bullet Time
MF's Ultimate, If you can get a W on the opponent, and get a nice set up for this Ultimate, they will not be able to escape due to Rylai's slow, and they will take all the damage done. Now let's compare the Ratios for AD and AP for this ultimate, *Takes out Asian calculator*
AD MF Usually gets a Bloodthirster, Infinity Edge, Frozen Mallet and Black Cleaver or some other AD damage item, MF's Ultimate has an AD ratio of 50%, So if you add all that together you get (100+80+20+40to50)/2, That is at least 100-120 Damage.
AP MF if skilled, gets 20 Stacks from Mejai Or Arcangels, Rylais, Lich Bane, Malady and Rabadon, That adds up to (650 to 800)/5, From your ultimate, you get 130-200 Damage. Don't forget you get a slow from Rylai's, allowing the skill to hit more. And with Malady stacked on them and Magic Penetration, you can deal large amounts of damage.

Start off with a Doran's blade, Farm and last hit,
save all your money up for a Malady
Pick up your Sorcerer's boots
Get a Mejai if you are doing great, if not work on Lich Bane
Get Rabadons
Work on a Rylai for tankiness
If you dont have Lich Bane, get it, And if you didn't grab Mejai, It's recommended to grab an Arcangel for skill spamming and spell damage, but the sixth item can be whatever you please.

Solo/Mid Lane
Early game
Harass with E and try to land some hits when you get impure shots, But for now, try your best to last hit every minion so you could grab a quick Malady, try to stay in lane until you have enough money for a Malady. Check for ganks on bottom and top, and always enter with your E.
Mid Game
Farm, but not as much as before, and focus on getting kills and helping team mates, If you have Mejai, try not to die and get stacked by at least assists.
Late Game
You are probably being aimed by now, Wait for everyone to go in and stay afar, Make sure it is safe before you start attacking.

Double Lane
Early Game
Harass with E and try to land some hits when you get impure shots, But for now, try your best to last hit every minion so you could grab a quick Malady, try to stay in lane until you have enough money for a Malady. Check for ganks on bottom and top, and always enter with your E. Try to be in sync with your lane partner, It is great to have a lane partner with CC's and can deal damage to get that first blood and harass.
Mid Game
Farm, but not as much as before, and focus on getting kills and helping team mates, If you have Mejai, try not to die and get stacked by at least assists.
Late Game
You are probably being aimed by now, Wait for everyone to go in and stay afar, Make sure it is safe before you start attacking.

I choose Ignite and Exhaust, With this you should be able to get an early first blood, and shut out their most annoying carry.

Masteries,
Self-explanatory, Armor Pen and damage just for farming, and more overall damage output as well as grabbing the experience boost from Utility.

Runes,
I usually get Movement speed quints to be able to have more mobility and chase more often, But I get MR Glyphs and Armor Seals to take care of her squishiness and Magic Pen Marks.