How do you study openings?


MCO is a reference work, not a textbook. You're trying to learn English by memorizing the dictionary.
As a first step, get a book with great explanations (I am a fan of Fundamental Chess Openings), read at will, and play games. After the game, look up the opening in FCO, and see whether you could have done better.
By the time the opening knowledge of you and your opponents outgrows FCO (think years), MCO might be useful. Or not...

All these advices here are good ones. However, I would like to make a little imput:
- if you are using a game database, go through the unnanotated games no more than 5 minutes, at least the first time. 10-15 will take forever; you can spend that time if they are annotated though (annotated but not the opening, the whole game).
- You will find repeated maneuvres, for both sides; try to get that, writing them down or just saving them is another base.
- If you can spend some time playing turn based tournaments here, great, try to get into some thematic tourneys.
- Play "thematic" blitz; youll get some experience and feel out of that. dedicate some days to play your pet lines, even if they are kicking you btt. Later, you can go over the books/databases.
- discard books/surveys/databases that only offer moves and none or little verbal explanations.
Good luck!
PS: I realize some things I wrote someone already did it, (Stragon was very detailed, for example) but, well, you have it here numbered!

play stuff you can force, until you can force your stuff no matter what. Forget all about the semi-slav, ruy lopez, main line sicilian, etc. until you have some sound-ish things you like to do on move 2 or close to it to force something that you are familiar with. Gambits. Then tackle the big ones that involve learning a lot of sidelines, transpostions, and unclear plans.
Quay-Z I don't think you addressed the original poster's question.
I like to study openings by playing games (working out the openings on my own) and then going through a database of master games from that opening and learning the ideas and plans. The drawback is that I quite frequently encounter lines I don't know, but by using similar plans I have seen from other experiences, I can usually formulate a decent enough plan.

You need to understand the openings you play far more than you need to memorize the first 8 to 10 moves. At the level of the OP I think the MCO and other opening "bibles" are quite useless and may do more harm than good. Its better to get something like Ruben Fine's " Understanding the Chess Openings" at the level the OP is now imo. You should go over complete games involving the opening(s) you choose to play so that you also have some idea of how to play the resulting middlegames and endings that often arise. Remember, your only goal in the opening is to reach a playable middlegame. IMO, the middlegame is the real meat/heart/soul of chess .
I have MCO 15 and have started to study in greater detail the Ruy Lopez and The Scotch for white, and The Pirc and The French for black. So far I know about the first four moves in the mainline for all of these. But I was thinking that I would like to know how to play these openings in greater detail so I thought about just opening the MCO and just playing through the moves line by line.
Is this how others study openings?