Happiness might be defined as a phenomenological state that's intuitively grasped to be valued for its own sake. It seems more appropriate to say that happiness isn't something that can be defined in an *objective* sense, but rather the very standard that helps us define things of value. That is, when we say that something is "good" and something else is "bad", we're speaking of phenomenological states aimed for in themselves and states avoided in themselves. The assumption is that the good is autotelic -- it has its end in itself, and is worth it "just because" -- intuitively. More fully, happiness is the self-evidentially (or intuitively) valued phenomenological byproduct of seeking to fulfill one's aim for things for their own sakes. This is probably why happiness involves not caring for happiness in the process of seeking it. "Seeking to understand happiness" is usually not happiness producing, because the goal of understanding happiness (thinking philosophically) usually doesn't involve a valued phenomenological experience. But, hey, it does right now as I'm in the process of understanding it -- although it's beginning to get a bit frustrating, and other meanings are beckoning my call.
So happiness isn't really something you can explain to another person, given its phenomenological nature, much as you can't explain love to someone who's never been in it before. You can only set them loose to trust the validity of their senses in determining whether any experience, and with it any thing experienced, is more or less "worth it". Happiness presupposes trust of one's senses, given that it's ultimately phenomenological. There's a dangerous tendency to turn happiness into a formula, whereby a person who fulfills the formula is by definition happy -- without resorting to any sense justification. And so someone can believe, through accepting his culture's values, that having material goods and a compliant, pretty wife is what the big picture's all about, while simultaneously suffering from despair. This is also a common occurrence for people in denial, such as alcoholics: they don't trust their own sense experience in some parts of their lives (particularly the ones that don't involve drinking, because this could mean confronting the fact that drinking isn't something that's worth it, and thus something that should go, and this is hard work because of the addiction) and so fool themselves into thinking their formulaic understandings of a happy life really are satisfying to them simply because they've been defined this way.
As for its fleeting nature, that all depends on the constellations of goals you have that hold the goods you've experienced in the past. The most cliche solution is to seek the meanings that are apparent to you now and see where that ends up. When you retrospectively analyze your experience, was it valued in itself according to your senses? If so, it's good and well for your catalogue of happiness states. And of course, some experiences are more valued than others. One of the more empirically validated treatments for depression involves getting people to analyze their current routine experiences and rate them on an hour block time sheet for a week, and then later come along and plan new activities that had in the past given them pleasure or mastery (two main symptoms of happiness) for the upcoming week and consequently rate them after trying them for a week. It's simple and powerful because it gets to the core of the problem: seeking happiness-producing experiences to replace previously non-happiness-producing experiences (or experiences with less amounts of happiness). The whole idea revolves around, again, trusting one's sense experience.