About the Author:

I've been playing League since late spring of 2011.
I've hit Diamond in Season 4, and had a break after the juggernaut update was released in Season 5.
I've returned about a month ago and am Plat IV at the time of writing this guide.
I play in the EU West server, and my in-game name is 'FNC Mister Titus' (yes, I'm kind of a Fnatic fan boy)
I main Mid and Jungle, with my favorite champions being Gragas, Lee, Zed, and Brand. I also occasionally play Vayne and Jinx in Bot lane.
I've never been in the competitive scene but who knows, eh?
I've been thinking about streaming for a while now, and I'll probably do so if I can wrap my head around how the software works.

is a champion that I've recently picked up after the new changes to the mage items.

I've always leaned towards champions that can determine the outcome of teamfights with their kit. Like that one binding that catches off a carry and nets you the victory with a 4v5 teamfight. Or that 4 man ult that tears through their defenses and forces the enemy team to scatter away from your ultimate.

I have so far had pretty decent success with Morgana in mid. Due to my generally safe playstyle, I don't take a lot of kills with this build. But I do serve the purpose of a battlemage completely. Since at the end of the day, the win matters more than your perfect score.

This build in particular delivers the promise of a tanky Midlaner that excells in a teamfight environment. Think of it as an upgraded version of a Morgana support.
Morgana always excels in team compositions that have a lot of hard CC. A Bard support, a Vi jungler, a Jinx ADC and a Maokai top would be somewhat of a dreamteam for Morgana.
This build however, is not the best for the thrill-seeker in mid lane. It is more of a control gameplay type that capitalizes on punishing enemies for making mistakes, and will ultimately pay off very well in the later stages of the game for your devoted patience.

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Some of my post-game results with this build:

Pros

Tanky
Good damage
Amazing team-fighter
Very good for kiting
Good for catching out enemies and starting team-fights
Good lane sustain with passive
CC immunity shield

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Cons

Skillshot reliant
Somewhat long cooldowns
Mana is depleted very fast if spammed
Lacks mobility
Short auto attack range

There are two sets of runes that you should consider before starting the game:

Runes vs AD Midlaners

This is your standard build against AD mid laners. You can also go for this runepage if the enemy team has an AD top and an AD jungler. Although I wouldn't recommend giving up Magic resist in the laning phase unless you are facing an AD mid.

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Runes vs AP Midlaners

This is a pretty common build for AP vs AP matchups, with the exception being the substitute of 9x for 9x . This is regarding the beefy nature of the Battlemage build. This will also help with survivability in lane past level 6.

FLASH:

Great tool for catching up on enemies, or getting away from sticky situations. A must have for almost every champion.

TELEPORT:

Whenever I pick Teleport, I find myself in better control over my farm and lane. I take Teleport against match-ups that do not require a specific counter-summoner spell (Such as Exhaust against a Zed). Needless to say, you also have the option to use Teleport for ganks and split-pushing.

EXHAUST:

Exhaust is a very specific pick for match-ups that rely heavily on short-term burst damage. It is also a very good tool when ganking and being ganked. Exhaust will also help you breach the frontline and take down the enemy AD Carry without taking much damage from them. An overall very good summoner spell.

IGNITE:

I usually find myself seldomly picking Ignite since this build isn't very focused on an aggressive playstyle. However, it might be a good idea to pick it against specific team compositions that rely heavily on self or ally healing. It is also a good pick against a Vladimir in mid lane.

HEAL:

I really do not recommend using Heal with Morgana when you have much better utility replacements such as Exhaust and Teleport. Also, you will already have a very large HP pool. Leave this to your AD carry.

BARRIER:

I believe Barrier is really a worse Exhaust. The idea behind both is the same, protecting you against enemy burst. However, you can significantly increase your chances of winning a skirmish with Exhaust while Barrier will only be helpful with negating a small portion of the damage taken. I do not recommend taking Barrier as Morgana

The ability sequence isn't concrete for this build. The only thing that you should always do, however, is putting 3 points into Tormented Shadow at level 5. Since this way, the full damage of the ability will be able to finish of the 3 caster minions in the back of the wave from full HP. This is essential for wave clearing and pushing.

If your team calls for an early invade, you should of course pick your Dark Binding at level 1.

From level 5, you may choose to prioritize your Dark Binding over Tormented Shadow. However, I find that maxing out Tormented Shadow to be optimal for pushing and wave control.

Early Game(Level 1-9):

Early game is nothing special for Morgana since your main focus will be to farm and push the enemy into their turret with your Tormented Shadow. This will be hard for melee champions and might cause most opponents to eat up their mana to clear waves.

Mid Game(Level 9-13):

Once you finish your Rod of Ages, your laning will be significantly easier and you will have no trouble pushing enemies while starting to dish out some pretty decent damage. As always, your main focus is establishing lane dominance. Since Mid Game is when objectives start to be contested and skirmishes happen, you might want to roam out and help your teammates wherever you can after you push your lane. Be careful for ganks since you will be mainly pushing and enemies will be more confident with their damage in Mid Game.

Mid-Late Game(@~min 20-30):

At this stage of the game, you are likely to have finished your Zhonya's Hourglass and have bought a Haunting Guise, and you will usually have about 6-8 stacks on your Rod of Ages. At this point, you are already more tanky than most mid laners ever will, and you have pretty decent damage. Look for skirmishes, stick with your team and contest objectives. Try to catch out mispositioned enemies with your Dark Bindings. Do your best to keep up in farm as you will want to finish your Liandry's Torment before Late Game starts.

Late Game(+30min):

Late game is when you reach your full potential and are a scary presence in your team's frontline. Catching off mispositioned enemies is more important in this stage than ever, since one Dark Binding can basically determine the outcome of a fight and ultimately, the game. Do not get over confident though, as champions like Kog'Maw and Vayne have percent health damage and can easily take you down if they focus you. Coordinate well with your teammate, and use your trinkets to spot and catch out enemies. If the enemy team ingores you simply because of your large HP pool, punish them by walking up to them and zoning their carries out with your Soul Shackles. You will likely force a Flash or even get a kill if they underestimate you.

Thank you guys so much for checking out my guide for Morgana.
I'm pretty new to this, and might have made a couple of formatting mistakes here and there :).
I appreciate all your feedback, be it negative or positive, and please share your results and experiences with this build!

Good luck out there!