This is the first time Im doing this so bare with me. Here you'll see how i build my Morgana. When i build her i try to Give her survivability with good all around ability power.

With runes I try to get as much mana and mana regen as possible in marks, glyphs and seals but I get a AP, Magic Pen and Health Quint.

As you can see above, i just get my relevant needs.

Heres where things get busy.
-Start with DARK BINDING in case the other team tries to gank you if you're soloing (Which i think Morgana is best at because I've never been out laned). Its also good for some early harassing.

-I start with DORAN'S RING because its really helpful. When im not losing mana by using my abilities, im getting more mana. Morgana should be playing it safe early game to farm, so its perfect. I try to solo as much as possible to get as much gold as possible, and with Morgana, getting gold is like taking candy from a ******ed baby. Shes THAT good at farming.

-If you keep leveling up TORMENTED SOIL early on in the game and keep your distance from enemy champions, they should get injured by walking over the soil while you're farming minions. And if they do end up harassing you, spellvamp from your TORMENTED SOIL should keep your health up. By the time you reach Level 6, if they havent gone back yet should make for an easy gank with your Ult. or your team mates.

-When you've farmed enough and have enough gold to buy basic boots and a NEEDLESSLY LARGE ROD go back and get them. By then you'll be destroying champions. If you have enough gold to get SORCERER'S SHOES as well, then get those too or get them on your next trip back.

-After getting more gold from kills and more farming, got right for RABADON'S DEATHCAP. It should give you enough Ability power for a couple of levels.

-Heres where things get interesting. Now you have to look to see what the other team is building. Are they building Magic Resist? Attack Damage? Ability Power? Or do you just want to get more survivability?
What to get when the other team is Building Magic Resist: VOID STAFF
What to get when the other team is Building Attack Damage: THORNMAIL
What to get when the other team is Building Ability Power: ABYSSAL SCEPTER and/or BANSHEE'S VEIL
What to get when you are looking for Survivability: WARMOG'S ARMOR

-When you are able to survive youll want more Ability Power. With ZHYONA'S HOURGLASS you should get a little more survivability and a bunch of AP.

-From there you have an option. Do you want to go TANK or AP? I sell my DORAN'S RING by then and try to go for a ROD OF AGES for some extra of both tank and AP.

-Dark Binding: Its good for snares early on in the game and nothing more. Once you build your Deathcap, it'll be a snare that also does a good amount of damage. You can also shoot it through walls, which makes great for ganking.

-Tormented Soil: This should be leveled up all the way first because its your tool for farming. Its great for farming and getting running away champions with low health. Also its great to put underneath in non-moving fights. With a lot of AP, it can do A LOT of damage. More than you think.

-Black Shield: Its great when you're laning someone with AP. It only blocks ability powers, so make sure whoever is getting attacked is getting attacked with AP. It doesnt need to be leveled up too early because the more AP you have, the better the shield is.

-SOUL SHACKLES: The Level Six ability. Or "Ult." is extremely powerful and gets stronger with more AP. When you use it, make sure youre not standing still or you might die. And try to stay in range. ONLY USE THIS WHEN THE CHAMPION YOU ARE TRYING TO KILL HAS LOW ENOUGH HEALTH OR WHEN YOURE RUNNING AWAY FROM SOMEONE THAT IS CHASING YOU.

Its not hard to play as Morgana, but its tougher to play GOOD as Morgana. The key to Morgana is to not be aggressive until you see an opportunity.