There are so many ways to help. For example: why don't we just make money and give it to them?
It's a very complicated issue and the problem isn't simply about generating money...
Obviously the first issue is how to distribute the money. Many of these governments are corrupt and high-rank officials end up pocketing the money themselves. Even if the money does go to the people, it is only a short-term solution. Sure, transactions increase in the short-run, thus stimulating the economy.
However, what is going to guarantee this continuity in the long-run? If not enough of these spendings are directed towards infrastructure investment, it will impede further growth in the economy. When the economy stagnates again, are you going to give money to these people again? Obviously, ideally you want to the initial money injection to kick-start the flailing economy so that it can run on its own toes.
In the above scenario, we haven't even talked about the possible shortage of supply of goods due to the sudden boost of money supply. Static supply and a sudden burst in demand growth will push prices up. So with all that extra cash, you'll end up with the same amount of goods anyway.
What this highlights is the fact that not only are these countries short of money - they are also poor because they lack resources and materials to begin with!
It is as if the government want to see these poor people suffer! I find it quite sad. Does anyone else agree that we and/or the government should do more to help?
There is a branch of economics called Development Economics that attempt to formulate the best response to this issue. They are slowly achieving results in certain countries such as India - although it is interesting to note that the majority of such economists today are of Indian/Sri-Lankan background (e.g. Amartya Sen).
So anyway, to help such countries, you can't hand out money to the public just like that. A Keynesian solution would be to get the government to build infrastructure. This will provide employment to the people of such countries, attract investors into the country etc. so it will be economically beneficial in the long-run.
Institutionalist economists will probably look at the current state of population welfare (especially nutrition and health) and will argue for the creation of government-funded health and education institutions in order to improve human resource qualities. Nutrition itself is actually a sub-subject of Development Economics research. Same with education.
Among the most interesting is the finding that in India, for every extra year of education a mother has, her child will be taller by half a centimetre (from what I remember). The argument is, literate mothers are able to access information written in newspapers etc. and are more equipped to deal with diseases common in very unhygienic environments e.g. diarrhoea. Just the fact they know to get their children drink lots of water can help form fitter human beings in the country in the future.
...what I want to highlight there is, the issue is very complicated and is a subject of much research. Something should indeed be done to help these people, and I think it is being done, albeit very slowly - or the impacts are seeping through very slowly, depending on what/who you believe. In the above scenario, we haven't even mentioned government corruption, coordination failures, agriculture/modern sector...