Hello, this is my Diana build.
I play this char as an assassin, so she's a bit squishy, but deals TONS of damages, really ^^
Try to always have a tank top or jungle when you pick her, cause you would prefer not to engage the fight or you'll have many chances to die.

The philosopher's stone Helps you to have a few more substain in lane, and to give blue buff to your AP Carry if you're jungling; the gold/5 is also nice.
As a top char, you'll probably be facing someone with a hard CC, so Mercury's Treads will help you.
Hextech Revolver, combined with her Pale Cascade will grant you a great substain during jungle and fights.
Diana have really low cd on her abilities, so Sheen will really increase your early damages.
She's needs to burst, so Rabadon's Deathcap will grant her HUGE damages output ^^
Her passive Moonsilver Blade procs every 3 hits an deal a really lots of damages, we'll see how to use it later, but Nashor's Tooth will help you to proc it more.
Lich Bane will make her proc on her massive AP, so at this point you'll burst hard :p
Zhonya's Hourglass helps you to gain lots of AP, a few armor against AD carries, and a great passive wich can help you to not get focused, or wait your abilities to be off cd, and burst again :)

Ok, so now it'll start to be interesting ^^
Her passive Moonsilver Blade procs every 3 hits she does, even if it isn't on the same target. So always makes 2 hits on minions to load it before engaging an ennemy.
It deals heavy damages in a small cone in front of her, so check your position to use it as it's best.
Her Q Crescent Strike is the key of her combo, always place it before engaging, excepts if you're sure to kill him with your burst. It have a quite low CD, so if you failed it, wait for it, and place it well this time.
It deals damages, but it also reveals ennemies with the Moonlight, use it to check bushes.
Moonlight last 3 cd and your ult won't have cd if you use it on a target afflicted with Moonlight.
Moonlight can also be applied in the zone Crescent Strike cross before exploding. Sometimes it's better to deal a few less damages without the explosion, and have no cd on ult with the Moonlight.

Her W Pale Cascade is a great shield, and it deals aoe damages around the ball. Use it on as much ennemies as possible, so after using your E during a teamfight or after jumping on an ennemy with your Ult.

Her E Moonfall will grab every ennemies in an aoe around her, and slow them. Put 1 point on it before ganking, it's a pretty cool ability :)
It have a quite long CD, so use it only when the ennemy run back, or during a teamfight, to help your team to deal lost of AOE damages.

Her ult Lunar Rush is a long range dash, with a low CD, and without CD if the target is afflicted by Moonlight. So try to always place your Q before using it, it'll grant you a great mobility. You can also use it to escape on ennemy minions, or jungle's creeps with your Q R combo. After your Rabadon's Deathcap, always use your Q on tanky minions to escape with your ult, cause it'll probably One shot the range and melee ones; or use your R without Q if you're sure to escape.

So your combo will be :
2 hits on minions to load your passive, Q on ennemy, R, Hextech Gunblade's active, autoattacks, W, E, autoattack, Q, R, autoattacks, R on the ennemy or on ennemy minions away if you were diving. Try to autoattack as much as possible to make you passive proc, it really deals lots of damages.