Diana is by far the best champion I have played as so far, due to her melee basic attacks with insane AP-mage abilities. She is a formidable opponent in the right hands and can easily take control of the battle ground. In an average game you can expect to be 3/0 up in the first 6 minutes of the game playing mid.

Summary: This build will give you roughly 700 AP when full, based on different abilities this is a run down of the max damage that can be achieved by Diana.

Moonsilver Blade(passive) = 290 + 420
Q Crescent Strike = 260 + 560
W Pale Cascade = 84 + 140 (per orb that hits, max 3)
E Moonfall = 0
R Lunar Rush = 220 + 420
Lich Bane(proc) = 700
Ignite = 410

Using to Skill order Q R W E R Q the max damage that can be achieved taking procs and spells into account is 5400, ignoring MR. Since most players will not have HP higher than around 3000 even with some MR getting past your MP, your burst should easily take down any champion 1v1 in a rotation that takes 6 seconds! Because of her surviverability you can easy escape and wait for cooldowns which a relatively small!

Since Crescent Strike is vital to Diana's power, it is of the highest importance to be able to make the shot without fail! I will not insult your intelligence by telling you how to make such shots as it is something you should already know.

However this is something vital so I shall give you one tip, wait until the opposing champion is moving towards you and aim your shot just behind them, because the player is clicking towards where you are, they cannot move their mouse back in time to click behind and dodge your shot!

This image shows when not to make the shot!

Pros

+ Insane burst damage
+ Good surviverability
+ Good Sustain
+ Able to frontline in a team fight

Cons

- Susceptible to CC (Stuns/Slows/Fears/Blinds)

For Marks I take flat MP Greater Mark of Magic Penetration as a large amount of Diana's damage comes from Crescent Strike and Lunar Rush MP means that both these spells do damage nearer to the true damage values shown.

For Seals I take flat Armour Greater Seal of Armor as this gives Diana more durability early on in the game, allowing her to be more aggressive for ganking mid.

For Glyphs and Quintessences I take flat AP Greater Glyph of Ability Power and Greater Quintessence of Ability Power this is self explanatory as more AP means more damage for all spells and her passive, giving greater ganking ability early on.

I take the standard 21/9/0 masteries for an AP champion, taking all the AP boosts in the Offensive tree as this gives greater damage output for all Diana's spells and passive.

For the other masteries I put 9 points in the Defensive tree in order to give Diana greater durability in fights and give an edge in the opening game.

At the start of the game I take Boots and 3x Health Potion, this gives Diana the advantage of speed over her opponent as here starting movement speed is slightly higher than most, the potions give her getter sustain to farm early in the game.

Fiendish Codex gives her much needed AP for more power towards possible ganks and feed early game, also leads onto Nashor's Tooth later.

Sorcerer's Shoes give MP allowing her to cut through most champions MR at this stage of the game, effectively making her spells do true damage. The boost of speed also means she is faster than any other champion in the battleground, with the exception of those with Mobility Boots and Boots of Swiftness excellent for chasing down ganks.

Next Nashor's Tooth gives a bonus 50% attack speed, meaning her passive will proc more often and increasing her damage output significantly.

The next 4 items all have the same idea, give Diana as much AP as possible to overpower her abilities to the extreme as well as giving some nice side stats.

Begin with Giant's Belt as this gives her more life to be aggressive with, follow this with completing Rylai's Crystal Scepter

Next build Sheen and complete Lich Bane giving a nice little boost to movement speed and an overpowered proc.

Finally Rabadon's Deathcap and Zhonya's Hourglass each giving an insane amount of AP and a little armour for late game play from Zhonya's Hourglass.