There are two schools of thought on this question--and the chasm that divides them is deep and wide.
One group of people believe the answer lies in spending a whole lot of money on schools, clinics, and new drugs in poor countries. What keeps poor people poor is that--well, they are too poor to help themselves. So the best thing that we can do is increase the resources they have command over.
But then there are those who think that poverty is caused by not inadequate resources--which is after all sort of tautological--but with inadequate opportunities. People do not invest in education or in health, or save enough, because they do not see enough (private) returns to doing so. So the way to get them to climb from poverty is to enhance the incentives that they face to help themselves and their community.
If you are the first kind of person, you think development proceeds one school, one clinic, or one project at a time, and emphasize foreign aid as a key part of the solution. If you are the second kind of person, you believe development happens one policy reform at a time, and you think the answer lies in improving the market and policy environment that poor people face.
People in the first group have names like Bono, Angelina Jolie, Bob Geldof, Bill Gates, John Edwards, and Jeffrey Sachs. People in the second group have names like Abhijit Banerjee, Tim Besley, Francesco Caselli, Esther Duflo, Lant Pritchett, and Mark Rosenzweig. Guess which point of view gets the bulk of media coverage and of public attention.
To be sure, there are many differences of views among the development economists that belong in the second group. Some of these economists emphasize policies directed at economic growth, while others stress health and education interventions. Some believe governments are the problem, while others think markets have a way of going wrong even when governments are not screwing things up. There are also important methodological debates within this group on how to "do" proper development research. But these differences reflect the vitality of the field and the diversity of approaches it houses.
Which is why it is a pity that the general public sees hears so little from the second group. Mention global poverty, and most people start thinking of debt relief, foreign aid, and (perhaps) cheap pharmaceuticals. Never mind that most development economists do not think these are where the real action is. Hey, Bono makes for much better copy.
Bono and company deserve great credit for the enormous success they have had in consciousness raising, and for bringing Africa to the center of attention in the rich countries. But it is time that the outreach made a better connection with the research.