The Dalai Lama is particularly fond of a meditation that promotes taking on responsibility for others' well-being. It is based on A Guide to the Bodhisattva Way of Life by the eighth-century Indian scholar-yogi-poet Shantideva.
It might seem that, in the abstract, self and other are equal: self is one and other is one. But when, aided by this visualization, you actually consider what “other” is, it's composed of a huge number of individual selves.
But even in this scenario, you might assume that the motivations of the "other" side are just as self-cherishing as your own, and thus you find no qualitative difference between self and other. You might then be inclined to help all equally—including your own self-cherishing self. This is perfectly fine, as long as your nasty self amounts to just one and does not equal "other" in terms of number. So if there are five people on the other side, then you should consider yourself one-sixth, not half.
Or you might get stuck wondering whether this contemplation calls for helping others and not helping yourself at all. It seems to me that the win–win solution is to put the main emphasis on helping others, making altruism the motivation of self-improvement. What is being targeted here is the feeling of yourself being exaggeratedly important in the process of becoming happy. Everyone wants happiness and doesn't want suffering.
Or you might think, "I am more important because I'm figuring all this out, and I'll be able to pass it on to those who don't understand." I find it fun to let this type of pride just be, not try to oppose it, but to think, "Even this sense of self-importance is for the sake of others." Think this over and over again, and pride, which usually serves to hide your inadequacies, disappears. The self-importance becomes hollow and fades.
We can do a lot of little things for others as we go about the day. Provide a cushion for somebody in your meditation group who can't find one. Little actions mean a great deal to others.
So we can make a decision to notice how we can most effectively help those around us. With such a motivation, our activities have a true importance that is not self-centered. It's difficult to decide how much to give away, how much time to devote to others, but the basic motivation is clear enough, and that in itself, on a day to day basis, undoes a lot of problems.