It's always awesome to have a Morgana go Mid, unless the opponent's Mid is Yasuo or Zed (which is becoming more likely these days, which annoys me because I main Morg).
You generally want to go
and
to start, but
is also good...sometimes. I don't really see the merit in going Doran's Ring anymore.
Try to build
/
/
for sight, then switch your Trinket to
when possible. Building AP is almost always the way to go (sometimes having better defenses against hard-hitters or Assassins/Gankers works too), but if you see a teamfight coming
is excellent—plus the extra health and mana lets you stay out longer, meaning you can hold your lane better. The slow from it also comes in very handy in teamfights, especially when you have a Stunner like
,
or
, or a Slower like
,
, or
. Try to build
as well.
For Spells, you can forgo
since your Turret distance is small. I like to go
/
or
/
if you have more confidence you can get fed.
Morgana should Gank whenever possible. Always build/max her Q first, practice taking Last Hits on minions vs Bots to get as much gold as possible. Learn to know when to and not to use the Q/W combo, and know when to use your Ult to max efficiency. When your teammates need help, HELP THEM—not only are you the Mid-Laner, but as Morgana your Abilities can make the difference in most teamfights. Don't be too pushy in-lane, though; Morgana is not Tristana, and while the occasional few hits with minions is good you should pay more attention to potential Ganks and times to Gank.
Try to build her Abilities and Masteries to take full advantage of her AP and Spellvamp, though having Tier 3 Gold-earning Seals doesn't hurt (each one gives .25 Gold per 10 seconds, so having all 9 makes 2.25 per 10 seconds—13.50 extra gold per minute can make the difference between getting that item you need. Having CDR Glyphs is also very handy, since you can use your Abilities more often.
Hope this helps.