I know this can be a subjective question depending on the opening, but in general, should on spend time on a few openings at once or should one concentrate on one opening for a while and play it every chance they get? In general, how long should one spend on an opening, including the variations?
You're right about this being a very subjective question. I've read a few books (sorry, can't think of good references) that suggest choosing a very limited set of openings to begin with. Use this exhaustively in every situation you play, whether appropriate or not. As you attack and defend in a variety of situations you will begin to learn the merits of the position in greater depth than simply reading about them.
As for how long to stick with it, my best suggestion (and this is indeed subjective) is to stick with the opening until you stop being surprised. Once you feel you've "seen it all", you're ready to branch out.
When you begin to spread to other openings, you may find it easier to use openings that can be transposed to from the openings you already know. The similarities will help you adjust more quickly and give you greater flexibility over the board.
My plan is usually as follows:
Read an introductory book on the opening. Usually if I don't actually like it I've figured it out during here, and if I do like it then I have a good idea of the most basic ideas or plans. The "Starting Out" series is good for this.
Put all the moves into ChessBase and save it in an opening libraries database.
Play the opening on the ICC constantly. I usually spend about a week doing this, I'm trying to get about 100 games with the opening. After every game, analyze with Houdini to see where the opening/middlegame plan went wrong, even if I won.
Identify problem areas or variations and patch them.
If I'm confident with the opening by this point, then this is usually enough, and I'll keep playing it on the internet to get better and to memorize it. If there's a variation that seems particularly popular or problematic, then I'll look up GM games or analysis on it, look at it with some friends, and use Houdini to come up with creative ideas. I usually pick the ideas that seem most likely to throw people off based on the playing styles I've observed, not the ideas with the best evals. Sometimes I even voluntarily go into negative evaluations when positive evaluations were available.
If I'm still not confident, I try to figure out if it's worth hanging onto. I've never had it be worth it.
Eventually, if it stays in my repertoire for longer than six months, I'll buy more books on the opening that are more advanced, along with some monographs and ChessPublishing PDFs (if available), so I can not only supplement it with new ideas (so I can have multiple options if I play the same opponent multiple times) but also have an idea of what people are recommending for the other side. Furthermore, the satisfaction of being an "expert" on the opening, having read a large amount of literature on it, is nice.
That's probably overkill, but that was always my chess studying style.
You need to work wholeheartedly on 1 or 2 openings for at least half a year until you know both of those openings inside out and then move on to another 2. This is really the most logical way to get good as 'fishing' through an opening book and learning roughly how to play many openings won't do you much justice at all. tactics and endgames in the meantime will also help you improve both your creativity and your spacial awareness alongside a solid opening structure. Good luck!