This is the build that I use with Morgana and have been quiet successful with some of my best games include 12/1/6, 20/3/8 and 15/4/17.
I take Clarity because of her mana dependence early game, trust me it really helps and the improved clarity will help any other spellcaster you are in lane with, plus if you take clarity and get Archangle's early as sujested in the item build then you should never have to worry about mana for the entire game. I take ignite for obvious reasons (I usually take ignite on any champ that doesnt do DOT damage P.S. tormented soul doesnt count if they can move out of it) You may be a bit concerned that you don't have any escaping summoner spells but dont worry, Morgana has one of the longest lasting stuns in the game and if you need a quick getaway just bind them and run.
For the runes I mostly go with usual caster runes, magic pen, ability power per level and flat ability power. Now the reason I replace the mana regen seals with ability power is because she is only really mana hungery early game and with the build order here she will never have to worry about mana after she gets Arcangle's and the extra ability power never hurts....well never hurts YOU :).
Now for her skill order you should always start with dark binding for good early game harassment and plus you are more likely to get first blood with a stun at level one. After level one you should level tormented soul all the way in order to have better farm early game and better health regen with her passive spell vamp (trust me if you are looking to regen health dark binding isen't going to help much). Keep dark binding on level one unless you can't level it in which case take another point in dark binding. After you level up tormented soul focus on dark binding and leave black shield to last.
Now I know that it looks really strange not getting your last skill until level 13 but hear me out for a minute. If you are in lane against AP champs then by all means get it at level 4 or 5 but if you are in lane against AT champs and especially if most of their team is AT then the shield is useless and won't do s**t because remember it only protects against MAGIC damage. This way you only level 2 skills then you do huge amounts of damage to your opponents early game. (I have brought a chogath down to 1/4 health at level 12 using only dark binding and tormented soul)
Now to the items, most of the items chosen don't really need any explination(AP items stuff like that) but I just thought that I should explain some things. Firstly the arcangle's staff is alot more important then you may think it is. You may think that you can get good enough mana regen and more AP by just taking something like Morello's Evil Tome, but you are WRONG. Remember that the Archangle's staff already gives you 45 flat AP and add that to the 3% of your mana that is being converted to AP, keep in mind that you are also getting extra mana from the archangle's effect and from your rod of ages (this is why both these items should be optained before the deathcap). In conclusion do the math you are getting far more AP from the Archangle's then you are getting from the Tome, 68.5 more to be exact. Now the only other item that i think I need to talk about is the Crystal Scepter, the only real reason I take this item is for the extra survivabilty I get with the extra health and if you really think that you dont need it or you just want more AP there is nothing wrong with getting the Hourglass or another deathcap, although the slow effect is pretty usful. Another item that you may consider getting is the Will of the Anceints for the extra spell vamp and after experience with it and without it I have to say that it isen't really worth it. When you get into late game all this item does is take up space for another item with higher AP like the deathcap or the Crystal Scepter and you can just as easily get health back by using your tormented soul on minions, which by the way will be much easier and faster if you have more AP. Finnaly the boots. I take sorcerer's shoes just for the magic pen, you can take cooldown reduction boots because all her abilities do have long cooldowns but I perfer the magic pen in order to maximize my damage output.
Now I think the only thing left for me to talk about is some strategies. A very effective and well known spell combo with morgana is dark binding and tormented soul. Cast dark binding to freeze them in place and then we tormented soul directly underneath them; this will provide excellent damage output. The last and most important thing to remember is that morgana has spell vamp this is VERY us full when you are low on health as she can get back up to full very quickly by just using tormented soul on a group of minions. Also remember that if you are being ganked by 2 or more champs USE HER ULTI. I have survived a 3v1 by using my ulti because remember it hits everyone within a 600 radius and the more champs on you the more it will heal you for because you are doing damage to everyone around you and they are probably too distracted and cocky to see that they you are gaining health faster than they can bring it down.
Black sheild can be very usful when you are low on health and being chased by an AP champ or if one of you allies is being chased, simply pop your sheild and then bind your target to get away. Remember this when there is a Karthus on the enemy team and you see his ulti charge up, If you do then you have succesfully deprived the enemy team of a kill :).
Another combo that I like to use against opponents with more health is dark binding, tormented soul, soul shackle. If you throw out your darkbinding and just before it hits plant a tormented soul directly underneath the enemy followed by a soul shackel the enemy is forced to stand there while their health is quickly drained away. This combo can be used to effectivly take down tanks and can also be quiet usfull when going up against fed AT champs because you can stop them from hitting you and take them down as qucikly as you can.
Remember to check out my YouTube channel for upcoming League of Legends games.
http://www.youtube.com/user/Battalrin?feature=mhum
I hope you found this guide helpful and remember to "Make them suffer!"