I have played Diana for a few days now and i want to share my build so others can improve as well, it won't be a very detailed guide

You want to get as much damage as possible out of your masteries, that's why i suggest the 21/9/0 masteries that i showed you above.

I have tried out many different builds, but this one is what i found deals most damage.
"Boots, X3 Health Potions > Sheen > Malady > Ninja Tabi/Mercury Threads > Rabadons Deathcap > Giant's Belt > Lich Bane > Rylai's Crystal Scepter > Abyssal Scepter

Optional items that works are for example
Survivability: Wriggle's Lantern, Guardian Angel, Zhonya's Hourglass, Banshee's Veil, Frozen Heart, Wit's End

Damage: Nashor's Tooth, Hextech Gunblade, Bloodthirster, Wit's End, Zhonya's Hourglass, Guinsoo's Rageblade, Void Staff, Will of the Ancients

Diana is based around attack speed and ability power and because of this i use the following runes:
Potency quintessences and glyphs
Alacrity marks
Warding/Resilience glyphs depending on what champion i'm fighting

Diana's passive "Moonsilver Blade" increases her attack speed by 20%, it also makes every third attack a cleave attack which deals 20-290 (depending on level) damage, this scales .6 on AP.

I start by maxing "Crescent Slash", her first spell, which is a curved skill shot, i max it first since it's her primary damage spell, and it's her only range spell, i put one point in it at level 1, this scales .8 on AP, it's the only spell applying moonlight.

The second spell "Pale Cascade" gives you a shield and three charges which explodes on contact with enemies, when all three charges are spent the shield is refreshed, it deals good damage and good protection, i put a point in this at level 2, i also think this is Diana's best spell, the charges scale .2 on AP and the shield scales .4 on AP.

The third spell "Moonfall" is a crowd control spell which deals no damage but pulls everyone into you, very useful when the enemy is fleeing or against ranged with low range like Annie.

The ultimate "Lunar Rush" works like Akali's ultimate, you charge towards an enemy minion or champion, you should almost always apply "Moonlight" to them before using this since it's cooldown will be refreshed, this scales .6 on AP.

I'm not quite sure about Counters yet but i've found Kayle and Cassiopeia to be good against me when i play Diana, Diana is good against bruisers with no gap closers or late game AP's such as Vladimir, Olaf, Anivia