So this is a build in progress, been playing morgana for a while.
for early game i recommend the tome and the health pot since you should have enough mana regen from your masteries and runes. your first item should be the spell book so you start your stacks early(if you are getting killed early and often go for the death fire grasp).
spell book (self explanatory)
deathfire grasp (this is one of the best items for Morgana. it deals with the triple threat, giving much needed cooldown reduction, an extra spell which you should use right after your bind/soil combo, since your others are DOTs there dmg wont effect the over all dmg of the grasp more effective(tip from DEWO)
lichbane( this gives you almost an extra nuke when you throw everything off adding your ability power to your auto attack also making up for your long cool downs allowing you that extra bit to get that kill.)
zonya's ring (gives you your power, with all that extra ability power added to your spells if you have time to get it with increase your lichbane auto attack and give your dark bind around 1000 dmg at this point)
rod of ages (this is optional you can get if early if your team is getting killed a lot/ your getting nuked by them this will add a lot of health and more nummy ability power)
if you actually have a game that lasts long enough to get all items and manage to have full stacks you should have around 650-700 ability power which is enough to kill even the most hp tanked char.
these items compliment Morgana in every why if your looking to do a lot of damage on her. Use your ignite and deathfire grasp give you extra damage in between cool downs so your not sitting there with your fingers crossed.
beginning game: 1-6
solo (try to get mid as much as you can)
get your amplifying tome and health pot to begin with, usually your facing an ashe, teemo, sivir, ezreal etc. for the most part these champs have one thing in common, not a lot of health. i recommend to not attack at all (other than placing pool every once and a while for minion and scare factor) until your level 4-6 which ever you feel more comfortable with. when you feel you have the right opportunity flash over minions and bind them pool and then ignite them auto attacking them for extra dmg (use ult if you have it in the mean time) always remember after you bind/pool always shield your self from any counter attack that can happen this will maximize damage and if you can time it so your minions can attack them do so but don't kill your self waiting for that. if you kill them you should have over 800 gold at that point if you have been last hitting minions often enough get your soulstealer and start ganking.
(more will be added soon)
please post comments to hear your feed back on anything your unsure about or that i may have over looked thx in advance