Welcome to the fastest way to build glass-cannon Diana with optimal results.

Insight Marks: coupled with Sorcerer's Boots, you'll penetrate Mercury's Treads and deal some remarkable damage from early to mid-game.

Resilience Seals: reduces damage taken by ADC and minions/monsters/etc.. Another viable choice of Glyphs are Vitality (health per level) to give you a bigger pool of health to take damage, or ap runes.

Force Glyphs: Gain AP as you level, thus making it easier to clear creep waves for farming as well as add to your AoE damage in team fights. Other great choices are Warding, Shielding, Focus, and even flat ap runes.

Potency Quints: best runes for ap champs, especially for an ap assassin like Diana. Other viable choices are swiftness, transmutation, insight, force, flat health/armor/mr, and per-level health/armor/mr.

Full offense for ap assassin, speccing in everything related to ability power and damage.

The best AP items for an AP glass-cannon assassin in perfect descending order from highest AP ratios to lowest [see above items].

sorc boots = early game damage + helps penetrate merc treads]
Deathcap = 140AP + AP% [amplifies the rest of your ap from runes, masteries, and items]
Hourglass = 100AP [tanky-dps; amplified by deathcap]
Grail = 90AP [tanky-dps; amplified by deathcap]
Rylai = 80AP [tanky-dps; amplified by deathcap]
Void = anti-MR-stacker item

NOTE: Predicting enemy required!
Wherever you think your target's going to move next, set your Q's orb there and activate.
If enemy moves into your Q, use R to close the gap, and then use your W. If in middle of crowd of enemies, use E [especially when enemy's using a channeling skill, when you take focus fire, or when you need to slow enemies so that your team can move in for fighting.

TL;DR: Q->R->auto-attack->W->auto-attack->E(as needed)->Q->R->auto-attack->until your target's dead.

Flash is very versatile in that it can be used to escape or chase. You can flash through walls to prevent being chased and focused down. Anti-feeding tool, tbh.

Ignite: extra [true] damage, and prevents your target from out-sustaining/lifestealing all damage dealt by you and/or your teammates while killing you in a fight.

Ghost is also nice. It helps you chase and land more auto-attacks. You can't hop over walls with this spell, though.

Exhaust: great spell for reducing damage while reducing pressure placed on you by a harassing enemy champ. Can be used to chase or escape.

All other spells are okay, but just aren't as game-winning as the above spells listed/suggested, imho.

Deal as much damage as possible. Go balls deep and win your games because you're Diana, the scorn of the moon. No mercy for the guilty!