Morga has been around a while and everyone pretty much knows what she does. Just to summarize:

Traditional Playstyles: Straight AP, or Tanky Support. Most people get an RoA and I used to too, but the mana is really quite wasted on her since all she really needs is regen. And Catalyst is such an expensive item for what you get -- Banshee's(and tank build) is definitely a better choice if you buy catalyst.

RoA doesn't really improve her survivability all that much. She already has good HP gain and she can't be burst down early thanks to shield. She can take care of herself in the lane with just AP and mana regen thanks to her passive.

My early Morgana game focuses on movespeed, wards, and getting her AP up nice and high ASAP because it's really the only thing that makes her viable. I don't buy HP items because I substitute them with speed and wards. There are other supports that play tanky support better than Morgana (i.e. Soraka). With Morgana, you get awesome skills that don't scale all that well. She farms well, but needs the farm.

My overall playstyle focuses on out-meta'ing the other team's support, and securing victory during teamfights. This means warding them up constantly, buying oracle if my team needs to clear their wards, counter warding, etc...

Pros: Incredibly versatile skillset, almost indomitable lane presence thanks to passive 15% spell vamp and aoe, shield that blocks incoming cc and soaks up magic damage, 2 cc spells (tho hard to land), and being one of the best farmers in the game means you have lots of money to spend on wards. Buy Wards!

Cons: Wretched movespeed, useless autoattack, item dependent, not great lategame viability unless insanely farmed up, predictable, banshee's veil presents a problem for her

This is a weird combination, I know. The point here is to get your starting AP to just above 9. This will make it so that your 2nd lvl soil allows you to one-hit the back row, and your 3rd lvl soil clears the back row completely. This makes farming a lot easier because you don't even have to think about it. The magic pen marks are a no-brainer; they give you the most bang for your buck. The movespeed quints, while not critical to this build, compliment it as we'll be going Boots of Mobility. You do not need gobs and gobs of mana regen as Morgana will use only one soil per creep wave, and will not be wasting mana firing off a bunch of snares that don't land or that won't net kills.

Here's a brief summary:

+8.5 Magic pen: best marks for a caster
+3 % Movespeed: synergize with boots of mobility
5.75% CDR @18 : casters need CDR
+7 mp/5/18 : casters need mana regen
+9.7 AP : helps farm early game

9/0/21 is pretty obvious for a caster. Take the crit chance over the AP (since it's a joke). Your damage from those few proc'd crits will end up netting you more damage long-term.

Why take a point in Utility Mastery? Why not. You have to spend it somewhere... I also take the improved flash because I love flash. Do what you want, just make sure you max Perseverance, Meditation, Quickness, and Intelligence (duh). Don't waste points on expanded mind unless you're one of those weird mana-pool people that buy RoA........ Weirdos...

Teleport/Flash all the way. Flash will be your escape/initiate tool and is indispensable. Teleport will keep your turrets up and allow you to move around to all those wards you placed. If you were a good boy and warded up the jungle, teleport may land you buff steals. Scenario: Enemy team is going for dragon, you have a ward there but your team is still out of range. If you have hourglass, teleport to the dragon ward when your team is just seconds away. Pop your ult, hourglass, watch your team mop up.

Other viable spells: Clairvoyance and Exhaust.

Waste of time: Pretty much everything else. You may END UP putting out a ****-ton of damage, but that is not your main purpose. Your purpose is to use your farm to out-meta the other team, and your skillset to win teamfights.

Buy wards.

Boots of Mobility... This item is what defines my playstyle with Morgana. She is so brutally slow that sometimes I just want to jump off a bridge before I get them. Here is a quick reasoning for this item.

1. She doesn't really NEED the magic pen from sorc boots because: a. her shield doesn't use it, b. soil (your all-purpose farming tool and the spell you cast most) is primarily being used on creeps anyway AND already has an MR debuff. The magic pen is going to play a part when you ult and are going in for a kill. That's like 2 percent or less of the total time you're on the map. What is that magic pen doing for you the rest of the time? Nothing. We only take it in the runes and masteries page because there isn't anything better, everyone else does, and this at least levels the playing field.

2. Merc treads are a waste on her. You have shield, and yeah, it should be cast on your squishy but you should be playing it safe anyway, and if you're alone, cast it on yourself and run -- they generally won't be able to catch you if you have Mobility Boots. If you are getting focused down, play less aggressively. You are there to ensure victory, and that means getting your spells off, setting up kills, and protecting your squishies

3. CDR boots are nice, but...........

The movespeed bonus is it. There's really nothing else. Just try it. All of a sudden you are free. Free to roam around wherever you want. Free to ward...

You have got to be able to move around the map, and move around in battle. "But you lose the ms buff when you engage!" Exactly, and you should be choosing the time and place of engagement viz. warding/scouting. Look, no one can catch you really once you have these boots. You block incoming CC, you took flash like a good boy, and you never ever ever overextend anyway do you?

The movespeed bonus is about positioning, which is key for landing your snares. It's also useful for intimidation, scouting, and yes, warding. These boots are the hidden secret to playing Morgana. They will improve your snare accuracy (since you'll be able to close faster and move around creeps), increase your intimidation factor, increase your survivability, and increase your penice size.

Get Soulstealer ONLY if things are going well obv. I buy it in about 60 percent of my games. Usually works out, especially if you can get an hourglass too.

The hourglass is your other core item. You need this, especially if you got a soulstealer. Put it on a hotkey you can easily reach (I use '3') and pop it after your ult. Maybe you don't land the second part of your ult, maybe you do. Point is, you survive.

After that, I usually by a codex and go from there.

If you can afford it, get a deathcap, then proceed to finish your codex.

Get a deathfire if you can handle the extra button and if they are tanky. I usually opt for Morello's evil Tome.

FYI, the codex will put your CDR at 30 percent at lvl 18. Buy blue pots to max it out, or finish you evil Tome.

Priority goes to Soil (for farming), and Snare (for increased duration). Get her ult whenever you can obv. Shield comes last because, even though it's a great spell, the cc block is really all you are looking for early game.

Unless you are playing vs. morons, landing snares is a little difficult sometimes. Your missile is slow, is attracted to creeps like a magnet, has a slight cast delay, and makes a noise everyone recognizes. The positives?

1. It's a skill shot, check bushes with it. If the missile stops, something's in there.
2. It has nice range.
3. It can fire through any terrain. (you will land about half your snares this way)

Here's the thing. When you're in lane, don't try to land a snare without a set-up. If it won't net you a kill, it's a waste of mana. The damage isn't that high and the "reward" for harassment with snare is just not worth the risk of missing and/or hitting them where they can recover easily.

Once you hit lvl 6, try the old shield/blink/ult combo. If you can chase them for the second part of your ult and land the stun, landing the snare becomes pretty easy.

If you have a lane partner, wait for him to bait or stun.

Do not throw wild snares out there. It will waste your mana, diminish your lane presence, give the other team a confidence boost, and make you start to question yourself.

Buy wards.

Stay alive! I play Morgana very aggressively but also very tight. Morgana is great at making people pay for sloppy play and careless mistakes. You will likely be faster than your tank(s) because +5 boots aren't very popular. Don't overextend if you are chasing. Yes, your speed allows you a little bit more leeway in regards to overextending, but if your teammates aren't around to help, you're just giving them an easy kill. Try to stay behind a tank before a teamfight; only come out to flank and fire snares.

Try using your other spells to cause enemy champs to behave predictably. That is how you will land snares. It's hard to land one on an enemy randomly clicking around the battlefield. What you want, is for them to click their home base (flee). Hitting someone running in a straight line is so much easier.

People have automatic reactions to things, like, for instance, popping your ult. They either converge or run -- it's always one or the other.

They also have reactions to casting soil. Tanks will often ignore it, but squishies will always try to move off of it. Use this automatic response to your advantage. You have a long cast range with soil/snare. Try flanking to a squishie's left, and cast soil to his right; many times, he'll instinctively move left and walk into your line of sight (snare).

If he gets used to this combo, switch it up. Play mind games and be a bully on the battlefield. That's what Morgana is really good at with boots of mobility. She gets such nice farm that she can buy tons of wards -- I usually end up buying about 20 in a 30 minute game.

Use your map control and speed to keep tabs on where everyone is. Follow their jungler around just to make him nervous, he can't catch you anway. Back off and then chase when they back off. Be a bully, play mindgames.

Use soil to dictate where the enemy squishies can and can't stand during teamfights. It's your battlefield. Make everyone scatter, or, make everyone converge on you and let your squishies clean up.

Playing Morgana is about decision-making. Does your carry always run away and never makes use of your shield? Try putting it on your tank or initiator, or put it on yourself and flash/ult them. Remind your teammates that just because you snare their tank, they don't have to engage. Try and lure out a squishy or have someone else initiate the fight. If you have to do it yourself, so be it -- just remember to get all your spells off and pop your hourglass after your ult.

If you do not have hourglass:

Once a teamfight is inevitable, shield your squishy, soil their squishies, and move to the periphery to start firing snares. Once the initial burst is over, go ahead and pop your ult. The initial dmg is, quite frequently, enough to make the enemy team scatter. Isolate a squishy, wait till he starts running in a straight line, and snare his ***.

If you do have hourglass (i.e. "second man in")

You now have the ability to dictate teamfights with your flash/ult/hourglass combo. Let your team know of your intentions. If you can co-ordinate with your tank (Amumu, Malphite, Nunu, Galio), you can set up some brutal combos. You really want to be the second guy into the fight (after the tank). Soil them first, shield your squishy, flash/ult/hourglass, watch mayhem ensue. If the score is even or better (and why wouldn't it be), you will more than likely survive no problem. Once you come out of hourglass, move to one side or the other and try to land a snare on a squishy. If you can't or if they're already dead, start chasing down their tank(s).

Really this build is all about mobility and map control. Morga is one of, if not the best, farmers in the game, but her AP ratios are abysmal. Riot did this on purpose, to make it tough to carry with her. You aren't supposed to spend every last cent bringing her AP up to ridiculous levels because it just doesn't pay off. You should be sinking a lot of that extra money into wards. Warding mid to late game can be very dangerous unless you have the kind of speed the Mobility boots afford you. Once you have them, you are able to move around the map quickly, dictate when to engage and, keep yourself alive. Morgana is not an AP carry, although it's possible to play her as one. Her farm is wasted on a zero-support, straight AP build. Sink that extra money into wards wards wards.