To begin with, if your child spends a lot of time staring dully at screens, then you're going to have to be firm—gentle, but firm—about limiting that time. If he's texting at the dinner table, tuned out on an iPod during family outings, or on Facebook all evening, the massive inertia of all that electronic passivity may foil even the most inspired efforts on your part to cultivate interests and motivation. So, before you start setting goals and modeling the behaviors you want and all that, you need to be prepared to draw the line on technology-assisted distraction. And yes, of course, if your child is meeting regularly with fellow geniuses to build computers from spare parts while speaking a special binary language they invented in their spare time, that's different. That's an interest, not a distraction from interest. OK, onward.
Setting goals. You want your child to be motivated, but motivated to do what? "Anything but sit in front of the TV" is not a good enough answer. You need a short, manageable list of interests that you can encourage your child to pursue as part of regular family life.
The challenge for a parent is to lead the child to some interests and follow the child to others. It would be nice if there were such a thing as "sampler lessons" that gave a taste of dance, sports, musical instruments, science, gardening, and so on. The purpose would be merely to identify some areas to which the child seems to respond and that could be pursued further. But the concept is worth noting, and life does offer its own more informal sampler lessons. Your child does offer some clues as to what kinds of interests are more likely to take. Does she have a feeling for animals? Is he into martial arts movies? Why? Find out more, and look for the kernel of potential interest. She might end up, say, volunteering at an animal shelter or learning to ride horses; it might turn out that he'd be interested in knowing more about kung fu or how to make a movie or cooking Cantonese food.
Expectations. Establish early in life some reasonable, not-too-heavy expectations that the child, as a member of the family, will participate in the life and running of the household. Simple chores and duties begun at an early age, even if not really helpful at first, are very useful in this regard. They establish your expectations in deed rather than in the form of an abstract sermon.
There is a continuum that runs from no expectations at all ("Let 'em be kids; this is the only time in their lives they'll be able to do nothing") to prebirth planning for an 18-year campaign culminating in Ivy League admission. You can develop motivation as a habit in the middle ground, where daily life is shaped. As part of the routine of life, your expectation that your child will fulfill responsibilities that increase with age conveys the point that activity and participation are natural. Such expectations can be a powerful force to counteract any developing tendency toward lack of interest or passive moping.
Modeling. Parents tend to focus heavily on teaching the lessons of life by talking. They tend to pay less attention to their own ability to influence their children through modeling. Observational learning is more potent than you might think. In terms of psychological influences, modeling is equivalent to the forehand in tennis, your steadiest and most reliable tool. Thus, no matter how much you tell your child that you want him to have interests and do things, your own behavior in that regard is more important.
Modeling can be used strategically to develop character, interests, and motivation. For instance, if you have some regular activity outside the house that's not necessarily adults-only, get in the habit of bringing your child along. Museums, particular social or political causes, sports or exercise, volunteering—it doesn't matter that much what it is.
What matters is your going and enjoying the activity. Taking your child along and making a routine out of it can have enormous benefits in terms of motivating your child and also in building your relationship. The routine and relationship-building aspects might be accomplished by doing regular chores like grocery shopping together, but we're talking about an added goal of being together: to engage in activities that build interest and competencies, accumulated knowledge or skill, over time. The growth of knowledge and skill mutually nurture interest and the desire to get out of the home and into activities. We mention this under the heading of modeling because having the child tag along to witness your direct involvement can be extremely valuable.
Buildingcompetencies. Building competencies does not always require that you model or engage in the activities yourself. It is useful to help your child develop some skill, activity, or talent that can continue over many years and pay dividends in social engagement. Music lessons, for instance, not only build skill in an instrument, they also bring the musician into contact with others (jamming, recitals, school orchestras), which can do a great deal to build motivation. Although interests can be used to build competencies, this is a two-way street. Building competencies can build interest, which in turn leads to more motivation and activity.
Environmental cues. How can one encourage an unmotivated child to take an interest in anything? Slowly, in a low-key fashion, and with mini- and many opportunities.