Yet another Champion and the first I've felt confident enough to write a guide about.
This guide will focus on Diana as an AP mid carry.
She performs very well here and is able to keep her opponents pushed allowing her to roam and help pick up those ganks when needed.
Here are 4 of my games with her:

Pros:
Low Cooldowns
High burst
Tanky with her W
Great chasing capability

Cons:
Little escape
Mana dependant early game
Miss your Q reduces your damage significantly

For runes I take 9 flat AD marks, 9 flat armour seals, 9 AP per level Glyphs and 3 flat AP quints.

My reason for the AD marks is they beef up her auto attacks nicely early game making it just that much easier to last hit without relying on your passive or risking losing CS

The armour seals go well with her shield and will give you more time to just walk away from jungler ganks

And the AP quints/Glyphs to boost her skills without the necessity for a Dorans as a first item.

For Masteries I take a standard AP 21/9/0 build however you can also take a 21/0/9 if you're confident that you don't need the extra hp and resists provided in the defensive tree.

These Masteries focus on AP, Cooldown reduction and bonus damage

Another viable option if you feel you don't need the extra defenses would be to pump those points into Brute force, Alacrity and weapon expertise with the final spare point bringing havoc up to its max 3/3 this beefs up your auto attacks just giving them a lot more bang for your buck without the necessity for building AD items.

So to start with always go for the boots and 3 HP pots, without boots you're holding a sign above your head begging your opponents to gank you and deny you hard.

From here I build a kages lucky pick because it gives a small amount of AP and the GP5 which if you do get pushed around a lot helps prevent you falling behind however you should still be able to rack up CS with well timed/aimed Q's at max range.

Boots are highly situational but 9/10 I would get the mercury treads because CC is the bane of Diana's existence, one well timed stun or snare just ruins her flow and makes you a sitting duck.

Then I recommend building a Fiendish codex for the Cooldown reduction and mana regen and again more AP, also getting this item early massively reduces your dependancy on blue buff meaning you won't constantly be recalling for a mana top up if your jungler is blue dependant themselves.

Nashors tooth is a must have on Diana, it has attack speed (more passive procs) Cooldown reduction (3.6 second Q's with a deathfire on top? yes please) mana regen and a nice chunk of AP. Everything Diana could need in one item.

From here advance to a Rylais crystal scepter, build the giants belt first if you find yourself being harassed, or if you're pressing an advantage start with the blasting wand to keep your harass hitting hard.

Then we can finally upgrade our pick to a deathfire grasp, more Cooldown reduction, more AP and a free nuker on top of her Q R W E Q combo, most games I've had end around the time I reach this item.

Lichbane is an obvious choice on Diana, passive that does AOE (Lichbane will proc on all hit) plus even if used on a normal auto attack it'll contribute to a nasty amount of burst on a single person.

Finally a Rabadons deathcap, most people will ask why not build it sooner for its passive? the simple reason being if you and your team are doing well you shouldn't get this far, this item is a steroid boost to help you nuke down that pesky carry quickly, so the money is better spent on other items.

Ranking of skills are as follows : R > Q > W > E

When Fighting, during the laning phase Harass with a Q but early game do not do it recklessly, it takes a chunk out of your mana and can leave you defenseless, Upon reaching level 6 Hit with your Q, use R to gap close, while dashing hit your W for the shield and only use your E if they start to run away. Rinse and repeat until they are pushed/saved/dead.

Personally I recommend Flash and ignite,
Flash gives you that added escape which Diana is sorely missing in her kit (unless you Q + R to minions that are behind you)

And ignite for securing kills or shutting down people with high health regen/heals (Mundo, Tryndamere etc.)

Alternatives to ignite would be Clarity in case you find yourself having big mana issues and a jungler who will be taking most blues or Exhaust to prevent your laning opponent from escaping.

Spells I would not recommend taking are Ghost, Revive, Surge or Clairvoyance. I usually find they haven't got much of a practical use on her as an AP mid.

In short, Diana is a very mobile champion with the capability of focusing nearly any opponent down, however do not let yourself be drawn into an extended fight without backup as if Diana gets pinned down she will die. Don't forget to gank top/bot if you've pushed your opponent out of lane and try and get as many blues as you can with the help of your jungler.


P.s. As I said this is my first guide so any and all constructive criticism will be taken gladly and if someone could help me with the formatting and adding all the item/summoner spell pictures I'd appreciate it.