Diana is an battle mage/assassin (she's melee and AP). This is a solo top/mid guide, not a jungle guide, so don't read this if u plan on jungling with her. After playing her in the PBE, I have come to the conclusion that this is the best way to play her. With her tremendous burst potential, you'll be able to jump onto and almost instantly kill any carry.
Because mobafire doesn't include the deathcap's 30% extra AP in the total AP, wut is shown in the stats is wrong. Her total AP is around 695.

Note: Many compare Diana to Akali seeing as how both of their ults are dashes, but this is COMPLETELY INCORRECTTTTTTT. I cannot stress how different Diana and Akali are: Diana is much. Much. MUch. MUCh. MUCH. MUCH BETTER!!!!!

I find that it is necessary to outline Diana's skills, due to how combo-reliant she is.

Diana's passive gives her a passive 20% attack speed and makes it so that every third auto attack deals AoE magic damage in a circle around her (It does a lot of damage. Not kidding, this is perhaps the most op passive i have ever seen. Second only to mordekaiser's iron man huehuehue). With a full build, the additional magic damage should be greater than 700 DAMAGE!!!! OPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOP

Moving on...

Her Q is an arced skill shot that does damage to enemies it passes through and then explodes at the end of that arc to do AoE damage at the end of the curve (No, the 2 forms of damage do not stack. the AoE at the end is just to make hitting people easier). It also applies moonlight, which lasts for 3 seconds, and is something i will talk about later in this section.

Her W gives her a shield upon activation and creates three circles that orbit her, which, upon touching an enemy, explode dealing AoE damage. If all three circles explode, she receives another shield. Nothing terribly special here, so lets move on.

Her E is similar to Oriana's ult. It draws in all enemies around her and slows them by a large percent of their movespeed. It doesn't actually do damage, so it is solely meant for cc.

Finally, Diana's R is a dash that deals damage to the target enemy. However, if the target is afflicted by Moonlight, the moonlight is consumed and her ult's cooldown is reduced to 1 second, making it (when used correctly) a 2 part burst. Her ult also has a very low cooldown (20 seconds at all lvls), so spamming it is fine.

I use magic pen marks because ALL mages get magic pen marks.
I take armor seals to help me lane against solo topers (see as how most are ad bruisers).
For glyphs and quints i use flat AP for more early game damage.
With these runes, i can deal out a lot of damage early on in the game, but still be tanky enough to survive.
In the glass cannon build, I take attack speed marks and seals
Magic resist glyphs would also be an okay choice if you were going for a more tanky diana build.

I use a standard 20-0-10 mastery page, taking all the magic related masteries in the offensive tree, and going up to veteran's scars in the defensive tree. Again, more damage is the key for this build, and these masteries will help you be all the more powerful.
In the glass cannon build, I take alacrity instead of sorcery, seeing as how nashors and deathfire already bring you up at 40% cdr.
Having both attack speed masteries and attack speed runes can also increase Diana's damage output buy focusing more on her passive (As shown with the second build).

I take flash and ignite (typical mage spells).
The flash is for mobility and a ways to escape bring ganked (seeing as Diana's only cc is her E, which actually DRAWS enemies towards her).
Ignite gives you the extra damage u need to finish off enemies that manage to narrowly escape your clutches.
Other possible spells would be exhaust instead of ignite (To lock down a high priority target so they cant do anything while u finish them off), or ghost instead of flash (to chase or escape).

I start by taking Q at lvl 1, it being her only real harass early in the game.
At lvl 2 i take W for more damage and the shield that can help counter harass. However, if ur jungler is planing on making a lvl 2 gank at top lane, then getting ur E is also fine.
Lvl 3 i get E so that i have my full combo.
Then, I focus on maxing my Q, Taking my ult at lvl 6 and then focusing on my W, maxing her E last.
The reason for maxing Q first is to make her Q-R-R combo very strong at early lvls.

YOU MUST FARM
All of these items are rather expensive. Money is ur friend. You need to be farming all game long, only stopping to help in team fights and get kills. But make sure you are managing your mana pool. Diana is a champion that doesnt need to use skills to clear waves (due to her passive) so dont waste your mana on minions, save it for fights.

Wut sets Diana apart from other champions is her Q-R-R combo that i mentioned earlier. Her Q deals massive damage and sets you up for a double ult. Used in conjunction with her W, you should be able to insta-gib your target, or bring them low enough for someone else on your team to easily finish them off.
Also, the pull on her E prevents any actions from her targets, giving you even more time to deal free damage on them, or run away to safety.
With a nashors tooth, you'll have 29% cdr, making her Q have a 4 second cooldown and her ult have about a 14 second cooldown. With a blue buff or deathfire grasp, you'll be able to spam even more. With these short cooldowns on such powerful skills, you should have no trouble destroying anyone in a 1v1 situation.
Also remember to auto attack during the down time when your skills aren't up. The gunblade allows you to do 140 damage with each auto attack and the third strike creating a burst of damage totaling at (i think) over 700 damage if not even more. After one round of 3 strikes, your skills should nearly be up again, allowing for you to once again, deal massive amounts of damage.
If your in a bad situation, you can Q to an enemy (preferably a minion) and then dash to it. after one second, dash again (to another minion) and your home free.
The only problem with Diana, is that she is relatively easy to be cc locked. AVOID STUNS AT ALL COSTS!!!
Also, try not to engage any bad fights. Make sure u can actually kill your target and escape without dying yourself. Due to the lack of tankyness in my build, you need to stay safe and jump out only when you're sure u wont die.

Before a team fight begins, you need to position yourself behind the enemy team, so that you can reach their carry quickly and remove them with your Q-R-R so fast, he/she wont even know wut's going on. Then switch focus to other high priority targets and melt them.

Pros:

Very high damage
Hard to chase down
Easy to chase enemies


Cons:

Easily cc locked

Diana is a really fun champion. I suggest you try her when she comes out. Stay tuned for an update to this guide when she gets nerfed in the upcoming week, because she will get nerfed. I'm serious. Diana is probably the most overpowered champion in the game right now. Have fun :D

Btw, this was my first guide trying to use color in the text. Tell me how i can improve my guides even more in the comments and remember to vote :D