If you don't want to bother reading the guide, I'd advise you simply look over at the Ideal Full Build, Runes, Masteries, and Leveling Order.
(Assuming you don't need the information on how to PLAY Diana.)

Passive: Every 3'rd auto does extra damage

Q: Before attempting to kill someone, throw your Q on them. It does a good amount of damage and effects them with the 'Moonlight' debuff. This will make your ultimate have no cooldown the next time you activate it on them. Moonlight does not stack, but it can be re-applied with another Q if it runs out or you would like to ult them more than 2 times.

W: Gives you a shield before and after the orbs detonate. The orbs that spin around Diana do damage to enemies, minions, camps, that they hit. This damage will help burst down enemies in your combos, while also keeping you from taking too much damage. If you dive someone under a turret, your W can keep some damage off you assuming you did not use it in your combo (They were low enough to R and you did not have to do a complete combo on) The shield is pretty nice. It's not amazing, but it adds a good amount of bulk to Diana overall.

E: Pulls enemies, minions, and jungle camps into Diana. This will cancel skills an enemy champion may be using, and it can be used to keep them from getting out of your autos. This skill does not do any damage, which is why I do not get it while jungling until level 5, as it is a waste of mana against every camp excluding Skuttle. This skill has a generally higher cooldown at higher levels so you may want to exclude it from your combo if you do not need to use it to kill the enemy, so that you may use it on a enemy with more health that will not go down as easy or has a risk of escaping.

R: Diana's R, like Akalis, allows her to dash to an enemy, jungle camp, or even Dragon/Baron. It has an amazingly low cooldown, making it available for nearly anytime you go for a kill. It is advised you engage with your Q then go in with your ultimate, so that you can use your ultimate twice. If Diana uses her ultimate after the enemy was hit with Moonlight (debuff), the cooldown is automatically refreshed. When I go after an enemy I generally ult once, and if they do not die fast enough or I have a risk of dying myself, ult twice. -- Dianas ultimate, while it isnt generally an escape, can be used to dash over walls if their is a nearby jungle camp. Q a jungle camp, such as Blue Buff, then use your ultimate to dash to it. Your Q will give you vision, and your ult will be refreshed after use.

Extra Notes: Zhonya's active can be helpful sometimes, but don't rely on it. I don't find myself using it very often. Maybe pop it if you have a high chance of dying after diving hard.

+Overall Fast Jungle Clear
+High Burst (Getting a kill with your combo is generally pretty easy early game)
+Snowballs hard and easy to get fed and stay fed (After picking up one or two kills from ganking, your burst becomes big
+AP scaling; bulky like a fighter, plays like an assassin
+Great Duelist once fed (You can easily get a double with your high burst. 1v1 situations are naturally easier, in most situations.)
+Big comeback if you fall behind early game. You can't fall behind too big on Diana, because if she gets even one or two kills, her burst goes up significantly with Ludens/Rabadons.
+Pretty easy to pick up and learn. She does damage; even if you don't know all the technical things about her; even if you don't have a full set of runes, shes still no pushover.

-Cannot gank pre-6 (You can, but don't expect much to happen unless they're very pushed up)
-Grabbing more than two/three kills is difficult in a teamfight because you would have dropped your entire kit on the last few kills and your cooldowns are refreshing.
-Takes a larger amount of decision making (When to engage, dive, etc; how to use your combo and or when. Ie; "Do I Q first, or R and hope I can kill him fast?")
-Becoming a more popular pick as people realize how great Diana actually is.
-Few/No Escapes if you can't R onto a jungle camp or another enemy. This can mean you often times dive in, get one or two kills, and die fast. Diana is essentially that. A big ap nuke. You go in, get a few kills, and die. It's good, but if you aren't really into that, it may turn you off a bit or shy you away from her kit.
-Falls off a bit late game. Late game she becomes basically a diving assassin. You have to play a lot safer. Go in, get a kill, and probably die trying to get out, is usually how it goes. That's all okay, assuming you kill someone who's actually worth something.

Gromp > Blue Buff > Wolves (Back, grab your Stalkers Blade), Golems (Save smite for Red Buff) > Red Buff > Raptors ~ REPEAT / Small Ganks / Roam a Bit, etc

Run into lane, or have the laner engage;
Q, R onto them, W then E. E when they start to run from you for maximum effect.
If they aren't dead yet, R onto them again, getting more auto attacks off, etc.

Your combo should be: Q R W E R, with auto's, chilling smite, etc, inbetween.

When teamfighting as Diana, try to poke them with your high damage Q before the fight starts and before someone engages. If you see a carry (mid laner or ADC) out of position and you know you can grab a fast kill without dying, you may want to dive in if you're fed enough.

When the teamfight starts, Q a squishy and jump onto them with your R + combo. If they don't focus you while you're doing this, continue by autoing them down or getting back into a safer position to fight from. You can repeat this step to grab even more kills as they scatter before your high burst and bulk.

Continue comboing down squishy enemies. I personally like going for the squishy AP mid, ADC, Support if they are alone and you can make it quick, top laner if you know you can finish them quickly, and tank if you have friends to help you and they are alone.

Don't be afraid to use your flash offensively. Flash Qing and proceeding with your combo is another way to get nice kills. Flashing for a few extra autos, if you can't wait for your Q or feel they might go out of range, etc.

This is my first guide on MobaFire. I am a Silver I support main who picked up Diana after falling in love with her concept, lore, and design. Doing generally very well and carrying my normal games, I read many previous guides and watched many videos on how to do well. After playing her so long, I decided I would make a guide with all the information and experience I gathered playing her. I hope you learned something and got an idea on how to play Diana, Scorn of the Moon; and thank you for taking your time to view/read my guide.

Oshy.