Welcome and thank your for taking the time to read my guide. Morgana is a very useful Champion in all stages of the game. Her early - mid game is where her damage really shines and she can be a nuker. But in late game her damage dwindles down to the point where she is a support in a way.
There's not much you can do damage wise as the game carries on, unless you have the enemies morale down the drain and they surrender at 20.

I choose Tormented soil first because it is your only farming tool. You won't be able to do much without your Soil and you'll just be pushed back by the enemy if you take your binding first. Typically I don't use it until I'm level 2, in mid. But, if you're laning with a partner the best place to drop your Soil is on the caster Minions to keep back the Ranged Carry. It's also very good to help your Melee farm up.

Choosing between finishing up your Soil or Shield all depends on the enemy team. If they are heavy on CC then you should choose to max your shield out as well as your binding, leaving your Soil at Level 3.

A lot of items work on Morgana, but the most important are Sorcerer Shoes and Rod of Ages. Without the Magic Pen your spells won't do much damage and the enemy team will just ignore you or just take you down before you can take out them. Boots of Swiftness is nice on Morgana because she is really slow, but they aren't really necessary with Ghost.

You'll want to build Catalyst first and then Work on Rod of Ages after that. You have to become beefy first, in my opinion, to be able to live whilst ulting. You have to go in the middle of the enemy team to ult which means you will be focused a lot during the duration of your stun. So Rod of Ages is always a must on her.

After that it all depends on the enemy team. If the majority are DPS then after RoA build a Frozen Heart, you get the armor your need +mana and the cooldown, the passive is also great to slow down their DPS. After your Frozen Heart build a Zhonyas Hourglass to give you even more Armor. An Abyssal can be built in b/ween those but it all depends on the enemy team and if the DPS or AP is doing the most damage. Will of the Ancients is great on Morgana because of the Passive, which helps so much in Solo and survival. You'll also be giving your teammates some AP and Spell Vamp.

Soloing
What you'll typically want to do while soloing is wait for the enemy to initiate on you. They will typically use their CC to start, so once you see them glow orange that when you want to self-cast shield on your self and then ult on them. Once your ult begins Puddle below them, if they appear to be running away from you which they should be then puddle behind them and snare them whenever you have a clear shot. Hopefully this burst is enough to kill them, but if not then spam your spells again after until they die.

Teamfights
Wait until the Tank initiates and they are focused on others. This is when you want to walk between as many Enemies as you can and Ult. They will start to split up, follow the Carry if you have them Shackled. Drop puddle on the enemy as much as you can and snare as much as you can. Shield your carry or whomever is under attack/close to dying.