This build will help show the power of an AP Miss Fortune, and how it scales with team play. There are many people who don't know the power of AP Miss Fortune, so this guide will help you see the truth. I've gotten many trolls in-game raging over me playing an AP Miss Fortune, but in the end, I always do better, so hopefully with a bit a practice you can utilize her power with this build.

AP Miss Fortune
Pros

Team Player
Does massive damage in a large area
AP Items provide more Health and Mana than AD items
Early Game you do tons of damage with Magic Pen. and Ability Power.

Cons

Not as strong in 1v1 situations
If team composition is bad, you won't be able to do very well
Skills can easily be dodged if not placed/timed properly

AD Miss Fortune
Pros

Great for 1v1 situations
Can do great individual damage in team fights
Utilizes best late game

Cons

Isn't as strong early game
AOE skills don't seem as effective mid to late game
AD items don't provide much surivivablilty (Squishy)
Not much of a team player.

Hybrid Miss Fortune
Pros

Strong in AD plus has a bit of AP to support

Cons

Does not help the team as much. Just like AD...

For Summoner Spells I take Flash and Ignite.
Flash - I find this a must. Why? It not only helps you escape tight situations, but it also can help place your Bullet Time in the perfect position

Ignite - This skill is great for Miss Fortune, especially if you're solo mid with her. When that enemy mid thinks he can take you on, just pop out your Make it Rain, turn on your Impure Shots, and cast Ignite, and they are done for :P

Optional
Ghost - great for chase and escape, but not so much positioning. You can make it work, but I prefer the ones I picked.

Exhaust - This also works for those heavy AD hitters. It can slow them down so you can burst them down with your Make it Rain and Bullet Time, but like I said, if your team composition is good you won't need it. Your team should be able to wall off/disable so you can just destroy their hp.

For runes I go Magic Penetration Marks, Mana Regeneration Per Level Seals, Ability Power Per Level Glyphs, and Flat Ability Power Quints. These Runes pushes Miss Fortune's damage from Make it Rain and Impure Shots early game and later adds to her Bullet Time. The mana regeneration seals help push her ability to spam and farm the minion creeps while harassing the lane.

For my Masteries, it's simple. 9/0/21 gives me the standard AP masteries that lower my cooldown and increase my magic penetration.

I max Make it Rain first, Impure Shots second, Double Up last, and Bullet Time whenever I can.

Controversial Ideas
I've run across many people who rage, because I play AP Miss Fortune and they say that Impure Shots, is only good if you have lots of attack speed with the AP. This statement is true in the fact that it may let you do more damage to a single target, BUT like I mentioned above, AP Miss Fortune is a TEAM player. That means she isn't too focused on singling out targets. She's there to do damage to as many players as possible. This makes your assasin, carries, and mages' jobs much easier.

Another is the hybrid argument. Hybrid is decent, don't get me wrong, but I find that AP Miss Fortune better because 1) you can do more damage with the stacked Magic Penetration and Ability power, than you can with AD+AP. 2) Focusing AP gives you the ability to have a more variety of items in certain situations. 3) AP items offer more health than AD/Hybrid items.

Core Item Build
Haunting Guise/ Void Staff - The Haunting Guise will give you the health, ability power, AND magic penetration early game. This item is overlooked by many people, and I have to admit I was one of them. This item is great to start with and can be later replaced by a void staff.
Sorcerer's Shoes - This item + Haunting Guise + magic penetration runes = tons of magic penetration. By the time you get to this item (after Kage's Lucky Pick and Haunting Guise) it may be around 15 mins or earlier into the game and unless the enemy is a tank, they shouldn't have much magic resist, so you should be able to cut through them like butter with Impure Shots, Make it Rain, and Bullet Time.
Rod of Ages - Now this is an item that I overlooked for Miss Fortune at first, but then was brought back up to my attention after the need for more survivability to my build. This gives Health, Mana, and Ability power over time which is great for being able to stay alive longer and still do damage.
Rylai's Crystal Scepter - This item is a must. Rylai's Crystal Scepter does wonders to your skills. Not only does it give you health AND ability power, but it also gives you slow for your ulimate.
Rabadon's Deathcap - Now to top it all off, you grab a deathcap to give you more damage to destroy your enemies :D

The last item is up to you :)

Situational/Optional
Deathfire Grasp - This item is great too. It gives you ability power, cooldown reduction and allows you to do damage based off their hp. I like to grab this occasionally but not always.

Abyssal Mask - Great if you're going against a team with heavy AP. Gives you ability power and magic resist.

Hextech Gunblade/ Will of Ancients - In all honesty I do not find Hextech Gunblade worth the gold. It may give you spell vamp, lifesteal, AP, and AD, but if you're going a full out AP Build it's not really worth the cost. Will of the Ancients is much better off than Hextech. It provides spell vamp, and ability power for you AND extra for your teammates.

Other items such as Nashor's Tooth (which I would recommend as the last item if you don't have any need for the ones above), Lich Bane, and Guinsoo's Rageblade are all optional items that work with AP Miss Fortune too.

Build Order
At start I grab a Amplifying Tomb and a Health Potion. From there I try to farm enough gold to grab a Kage's Lucky Pick, Boots, Ruby Crystal, and if I can an Amplifying Tomb. From there I finish my Haunting Guise and then I finish my Sorcerer's Shoes. After that I go straight for Rod of Ages, followed by either a Deathfire Grasp or Rylai's Crystal Scepter. After I grab Rabadon's Deathcap and then grab my optional/situational item. From there, the last thing I do is sell my Haunting Guise for a Void Staff to top my build off.

Now comes how to utilize her in-game.

Laning
I personally take mid almost every game. Why? Because you get the creeps to farm. Your Make it Rain can easily finish minions at half hp at level 1, plus with auto-attacks makes it an easy farm. The build I assigned requires a lot of gold, so the more farm you can get, the easier it will be to destroy the enemy team. If you can't happen to grab mid-lane, try laning with a disabler. They are your best friend. With them stuck in your Make it Rain and later in your Bullet Time, it's pretty much over for them.

Farming
How to make the most of your farm? Place your Make it Rain around the melee minions(if you can), but more towards the mage minions and the champion. You want to try and hit both minion and champion whenever you can. If the champion tends to stay away from the minions, or is a ranged champion, just focus more on minions and throw in a few Make it Rain on them. Remember that Impure Shots can really hurt your enemy if they are pretty squishy. It may not seem like it, but it can do some damage.

The best team composition for an AP Miss Fortune, is one that has an AOE disable, for example Galio, Sona, Amumu etc. These will be your best friends. Others are single stun/disable champions. All of these will work well with your spells.

If your team has no, or very few disables, it may be a bit hard for you to do much, but if your team is good, you'll be able to do the damage and still win. This requires perfect positioning of your ultimate as your team engages the enemy. Remember, your job is not only to get kills, but to back up your team so they can destroy.

Positioning will take practice, but just make sure to not give up and don't listen to those trolls! :)

Playing AP Miss Fortune made me feel more part of the team, other than just a solo player. I hope this guide really helps those who want to play Miss Fortune a different way. If you have any questions or corrections, please feel free to PM me or leave a comment below.