Introduction to pain...
Morgana is a strange mix of awesome. I love her. She's got the gusto to nuke just about every champion in the game and still has enough care and consideration to lend a huge hand in team fights. She's a nuke, and a perfect lane partner. I've been playing her non-stop for months and I haven't found a champion yet to rival my love for her.
Lets get this straight right here...I do NOT play as passively as I should. I don't really need to, not with Morgana. This is why my runes are set up as:
Greater Marks of Insight x9
Greater Seals of Potency x9
Greater Glyphs of Potency x9
Quintessence of Potency x1
Quintessence of Wisdom x2
Now I can hear the haters rambling off at the mouth (or ***gy geek fingers on a keyboard) saying this is stupid. F*@k them. They're haters. No one cares what they think. The marks of insight allow you to penetrate natural magic resistance off the bat allowing more damage from harassing so you can sneak in a sneaky skill kill with Dark Binding. The Potency runes are that damage. The nuke dejour. Flat AP doesn't give as much as the Force runes in the long run, but that's what the item build is for. A measly 10 ap more won't do a damn thing late game. Anyone who tells you differently obviously had the umbilical chord wrapped around their neck at birth. Now, the wisdom quints are the "/all TROLOLOLOLOLOL" factor. You level faster than the person/people you're laning against meaning your resistances get higher, you do more damage, and you'll get your ultimate sooner than they. For this build, that means a LOT.
Masteries...The bland part.
Morgana doesn't need any different than any other caster in the game regarding masteries. The standard 9-0-21 works. Make sure to get the one point at the bottom talent in utility. I pick up the added Clarity for those brutal team fights and instead of having a point in strength, I put it in improved exhaust (because of the magic resistance debuff)
Items...the fun part.
I start with boots of speed, 2 mana pots, and one health pot. This allows me to avoid as much as possible, chase for that last hit, and to out lane. Next on the docket is the Abyssal Scepter. "But why? What good will that do against non-casters?" Shut up. It's another debuff. It lowers the champions magic resistance even more than what you already have for runes. Extra nuke power with a nice little AP champ block. Next is the Sorc boots. No questions. You need the movement speed, and yet again...another debuff. After that you must play it how it's being played. If you're taking a lot of **** from dps champs, Zhonya's Hourglass. If you're doing fine so far, Rabadon's Deathcap. Either way, those are your next 2 items. Rylai's Crystal Scepter is a great addition, especially for the slow and the extra health. Team fights can be not only contained, but torn the f&*k up because of the slow and the ability to endure more damage. Last, but not least...eh, forget it. You get the just of it. Like I said before, it depends on how the match is going. Find the item that gives you what you're lacking, and if you're not lacking, crate that AP through the roof.
Tormented soil is your bread and butter. You can survive, farm, obliterate, own, and build massive amounts of gold with this skill alone. However, you want Dark binding built up too. It packs a hell of a punch and when you're being chased, a quick spin and snare can grant you the health (From Morgana's passive spell vamp) to get the hell out of there. The Black Shield isn't has helpful as I hear everyone claim it to be. It only blocks spell damage which doesn't help with tanky dps champs much, but for caster's its great. Ryze is practically useless against the shield. Turrets will eat you for breakfast THROUGH the shield. Considering, as Morgana is a caster, she's likely to meet up with AD champs, Tanks, and turrets more than another caster unless you're tearing mid up. For the Soul Shackle ultimate...if you don't put a point in your ult as soon as it lets you, turn off your computer, find a brick, and beat yourself until the stupid leaves your body.
Use what you like to use. Morgana is a great harasser, but doing so drains mana like crazy, which is why I pick up clarity. Also, I use exhaust for the magic resistance debuff, but use whatever feels comfortable to you.
I have given you the Golden Goose Egg of my LoL experience here. Use it wisely, and enjoy those double digit kills.