This guide focuses on both of Morgana's Supportive and Offensive abilities. Hope you all like it :)

Pros

A great CC counter (Due to Black Shield
Very hard to kill
A big contribution to the team
Extremly Hard to Gank

Cons

Does barely damage in Late game(Unless really fed)
Usually targeted on team fights

The usual masteries

More AP, more Black Shield Strength and more damaging Dark Binding

Greater Mark of Magic Penetration Magic Penetration = More Magic Damage = More Spell Vamp

Greater Seal of Replenishment Well you cannot support if you're always missing mana and going back and forth to the respawning point is just a waste of exp.
Greater Seal of Ability Power For an early AP boost

Greater Glyph of Ability Power or Greater Glyph of Scaling Ability Power Same reason for the Greater Seal of Ability Power

For summoner spells, I recommend both Heal and Flash for beginners or those on duo lanes

Take Heal to help sustain your team mate since you're able to sustain yourself

Flash may it be to snare that running target or to rescue that dying mate, Flash really is very helpful

Ignite and Heal for those who are on solo lanes

Other Viable Spells:

Ghost Same use for Flash

Clarity Also great for sustenance but becomes a bit useless at late game

Teleport Great for getting back to a lane to defend or help an ally to escape or to kill

Cleanse Really great spell, though not as resilient as your Black Shield very dependable on helping you on those tight situations.


Never Take:

Revive May seem good but nah.

Smite Won't need it, Don't have it

Surge The AP boost you get isn't enough for wasting a slot of summoner spell

Promote Really why even think of taking it?

Clairvoyance This really depends on the situation, though I more likely advise not to take it

Exhaust You have tons of CC and I'm sure one or two of your AD carries has one

Innate

Soul Siphon

Grants 10%/20%/30% spell vamp.

One of the best Innates of the game. One of the reason why Morgana dominates most lanes

Abilities

Dark Binding

(Active): Morgana releases a sphere of dark magic. Upon contact with an enemy unit, the sphere will deal damage and force the unit to the ground, making it unable to move.

Cooldown: 11 seconds
Range: 1300
Cost: 60 / 75 / 90 / 105 / 120 mana
Magic Damage: 80 / 135 / 190 / 245 / 300 (+0.9 per ability power)
Duration: 2 / 2.25 / 2.5 / 2.75 / 3 seconds

Land this one and you're almost sure to get a kill. Though a bit hard to land because of the slow animation making it easier to dodge

Tormented Soil

(Active): Infects an area with desecrated soil for 5 seconds, causing enemy units who stand on the location to take magic damage and lose magic resistance every second they are standing on the area.

Cooldown: 10 seconds
Range to Center of AoE: 900
Radius of AoE: 350
Cost: 70 / 85 / 100 / 115 / 130 mana
Magic Damage Per Second: 25 / 40 / 55 / 70 / 85 (+0.2 per ability power)
Magic Resistance Reduction: 4 / 5 / 6 / 7 / 8 per second

Especially great for squishy opponents, though I max it last, it's still according situation if the enemy team is building magic resists early, I suggest leveling this skill to just level 2 or 3 earlier to counter them

Black Shield

(Active): Places a shield around target friendly champion, absorbing magic damage and preventing disables while the shield holds.
Lasts 5 seconds or until the shield is broken.
Cost: 50 mana
Cooldown: 15 seconds
Range: 600
Shield Strength: 95 / 160 / 225 / 290 / 355 (+0.7 per ability power)

An anti-gank, almost anti-death shield for team mates and yourself.

Soul Shackles

(Active): Morgana latches chains of energy onto nearby enemy champions, dealing initial damage to them after a brief delay of 0.5 seconds, and slowing their movement speed by 20% for up to 3 seconds. If the target(s) stay in range for the full duration of the slow, they are dealt the same magic damage again and are stunned for 1.5 seconds.
Range for activating: 600
Max range after activation: 1000
Cost: 100 / 150 / 200 mana
Cooldown: 120 / 110 / 100 seconds
Magic Damage: 175 / 250 / 325 (+0.7 per ability power)

A great Clash starter, though when cast, be sure to maximize it's potential by hitting the most(3) champions and also keeping them within range for the stun. But I should say that by doing this, you put yourself into a very vulnerable situation, so I advise to be careful.

Core Items

Rod of Ages A great item, that Mana + Health boost and a very not bad boost to your AP

Rabadon's Deathcap A must have on maybe every AP mage there is

Rylai's Crystal Scepter Added health and AP is always good

Other Good Items:
Frozen Heart Nice bonuses though a non-AP item, it's still a good buy, gives you tankiness and great against AD champions

Mejai's Soulstealer If you're confident that you can keep the stacks, then go for it

Zonya's Hourglass Great against an AD heavy enemy team and also helpful to cast your ulti without dying

Thornmail Another great Anti-AD item

Deathfire Grasp Useful to bring those tank's health down

Will of the Ancients A nice AP boost and a spell vamp. The aura is not bad to. Very useful if your team has 2 or 3 other AP

On picking a lane, check which ally you would be more useful with. For example your team composition is:

Urgot
Amumu
Morgana
Vayne
Akali

and your team's Urgot was decided for Mid lane, with your remaining allies, you'll be more likely a great help to Vayne rather than the other 2 since with your Black Shield she would be able to get near your enemies while not suffering much CC and magic damage and that snare is also helpful for her to position herself to initiate a good Condemn. Greatest Ingame Tip: Know your allies and enemies, If you know their strength and weaknesses, you'll be a great help to your team.