CORE:

The core items are chalice and Zhonyas. Zhonyas is the more important item for Morgana, as it allows you to jump on the middle of their team, ult, and get out alive. Chalice is very good, not only because it gives you enough mana to allow you to spam you q while camping a tower (morello's is not enough to do it) and farm with W and M.R., but because the GRAIL also gives you 20% CDR, and with blue, you can get the 40% M.R cap. Also, with grail you generally don't need to build more M.R. (your shield take care of the rest).

You can build rabadons, void staff, or finish the grail now. This depends of the team you are facing and the status you want more. If the are >A LOT< of ap in the other team, u can consider buying an abysal septer, but it will hurt your damage in a way. If you do, i think is worth to buy Liandry's torment and don't make void staff at all. U also want enchantment: distortion, as flashing in the middle of their team, ulting and popping zhonias is fun, a great initiation tool, and you want to be able to do it as often as possible.

For the end game:

If the game goes for ever u can choose to buy one of those itens: Rylais may looks very bad in Morgana but if you are being focused, you and more life. This item is the only one that gives you a good quantity of life. Also, it makes your tormented soil slows them, with is cute. Morelo's helps you get 40% cdr if you are not getting blue, and frozen hearth is a very good option if you REALLY, and i mean REALLY, need to be tankier. If eveything is going fine you can choose between WoA, DFG or liandrys. DFG can help you if u need to 1x1 a lot, liandrys is very good against a team with lot's of bruisers and WoA is the best option in any other occasion.

For abilities, u should put a point in dark binding at lvl 1. It helps with early ganks and a possible invade. After that, put a point in tormented soil and black shield. getting soil at lvl 3 by level 5 is very important, as it allows you to one shot their minions. I like to level my shield second, as it helps to do fun things in lane, makes you tankier in TFs, and helps you to save a team mate sometimes. Also, with ignite, your full combo and 2~3 basics you can one shot most champions by level 6 any way (Be careful if they have a lot of M.R.).

If you are lanning against an AD, put a point on black shield and UP dark binding second.

Masteries

U really want your flash in a low CD, so 9 points in utility is very good. Also, one point in Artificer helps you to poop your zhonias more often.

Runes:

U want to dive in the middle of their team with zhonias, so armor and m.r. runes help a lot. Starting with two mana potions and fairy charm, u don't need maga regen in the runes, so u can choose between armor and health per lvl on the seals. You can also get AP. per level gliphs if you want.