Welcome to Morgana101.

I main support and she is definitely my number one pick. This build is focused around zoning the bottom lane and forcing their jungler to camp. This gives the rest of the map less pressure allowing them to farm and carry.

Pros:
Dominate with snares, stuns, and heavy damage
Feed your team to victory
Very High Sustain
Good Ability Power Scaling for abilities
Black Shield (E) prevents CC from working on a single target basically nerfing the enemies combos
Cons:
Finding an adc good enough to play with is very difficult
You have to rely on teammates to be able to play the game well
No escape mobility other than Ult + Zhonya's active or snare
Not good range

Most people won't like to take teleport on a bottom laner, especially as a support. Though, Morgana always being in lane is perfect for both overwhelming presence and constant poke. While the adc is running back to lane you can punch them in the face and snare them under turret.

I choose exhaust over heal because it weakens their damage output and slows them just in case I miss my snare or want to ult them. Heal is very viable instead of exhaust, but offensively exhaust is far better.

Runes selection is quite large. Finding the right runes for everyone is difficult and most people don't have more than the two runes pages. Though, Morgana uses the basic rune page effectively. Early armor and magic resist really offsets the enemy because they do so much less damage than normal.
The reason behind getting both armor and magic resist is simple, you'll most likely be facing both in the bottom lane: adc + supp.
Magic pen. is great for her powerful poke snare (Q). It allows you to scare them away from farming due to how much damage they'll have to take just to get any farm at all.
And the ability power quints speak for themselves. She has very little base ability power (0 I think) and early power + pen is really agressive and allows you to freeze them while your adc takes all the farm they want.

Morgana's mastery page is very 'support basic'. It looks a lot like the other support's mastery pages, but, for Morgana you need to focus on cooldown reduction and gold income. Mana Regen is built into the item set, so, plenty of cooldown reduction allows for a constant supply of annoyance.
Movement speed is also important for catching up to enemies, or friendlies, but in the utility tree "Wanderer" could be traded for "Bandit" it is entirely preference.
Her sustain is nice because of her passive, starting her off with and immediate 10% spell vamp, but since you will be a tankish support with annoying, scary poke you will often be poked back so, having the biscuits is a good idea.

Soul Siphon (Passive)
Morgana is granted 10% / 15% / 20% bonus spell vamp.

To Survive Early Game:
Use Tormented Soil (W) to suck the life out of minions but be careful not to steal your adc's farm.
You will end up pushing farther faster when doing this so dont over extend, be weary of jungle ganks. Ward Ward Ward


Dark Binding (Q)

To Be Successful with Morgana: Land the snare. It is the biggest damage attack you have and it sets up well with Tomented Soil (W) and your adc attacking them. OR, it could simply be a poke. It is great for scaring away enemies due to its high damage.


Tormented Soil (W)

As said before, use this to maintain health and in combination with your snare. This also works well with Spellthief edge and Bandit.


Soul Shackles (R)

This is your ultimate team fight move. It does wonders when pair with the Zhonya's Hourglass active(making invulnerable and immobile for 2.5 seconds) because it takes 3 seconds for the ability to proc off. With 140% ability power scaling and 650 base damage at level 3 you can really take it to an entire team. The most important part about this combo is you must activate the ult before the active because after the active has been used you can't do anything at all.