Being such a strong champion, you would try and say she gets everything in early game, but that's not true. Diana starts to own her lane after level 3, and totally counters everything with good farm and lane domination at level 6. Harass your enemy a lot with your q and try to farm without using much mana if possible. First back, with an exccelent start, would be to buy a needless large rod. and some boots and hp potions.

I'd suggest to leave the needless large rod where it is and just start working on your Lich Bane, starting with Shen and if possible trying to get it all the item by the next back.
Secondly, you'd like more speed and some magic penetration, so Sorccere's Shoes sounds good. Altough if you are the funny person, like I am, Swiftness Boots all the way.

Here things start to get fun. Rabadon's for the win. Get it!

From now on, you might call me crazy, but this worked our for me like GODLIKE mode ( and by other means, this is a hybrid build so here we go ), buy Hextech Revolver! :)

For our next op stage - Trinity Force. And I know some of you might call me insane because I know the Sheen from Tri won't stack with the Lich Bane, but it gives you a lot to play and poke around with, especially with her passive. So Trinity Force all the way!

For our last late game item, I'd go for a Banshee Veil in case our enemies are a bit fed or just if you wanna go really hardcore and don't give a damn. ( if you pick the Swiftness Shoes route, get the Void Staff). Othewise, just buy a Void Staff and prepare to do a masacre.

If you have any questions about how this build goes, well let's just say this is the ultimate Hybrid Diana build I could ever think of in my case. And it just covers all her abilities, gives you sustain and a big fine damage. So, just get in 5v5, 3v3 or 1v1 and own your opponent, because that's what you wanna do!

I'd apreciate your feedback!

GG, WP!