Good questions. There are a number of ways to do it, and they're each difficult in their own way.
Firstly, within a mixed-market system (colloquially known as capitalism), there are a number of things we can do.
* On a governmental level, a move away from the Thatcherite, free-market ideology that has poisoned our society for the last 35 years will help to reduce poverty. Higher taxation on the rich, high minimum wages, perhaps a Basic Income (agreed upon by economists of the Left and Right, for that matter), can help to reduce poverty in every country. In countries such as Denmark, they have a high taxation rate and a high minimum wage, and they have the lowest poverty and inequality levels. Economic growth in such a mixed-market system would mean that growth is distributed more towards those in poverty than it would be in a system closer to pure capitalism (which has never existed - every country is, at the very least, a mixed-market system.) The
more equal a society, the greater its rate of poverty reduction, as this study demonstrates. And,
the more equal a society, the better its economic growth. Since Reagan and Thatcher came along, inequality in the United States and Britain has shot up.
* On an individual level, there are things we can do as well. Donating even a small proportion of our incomes (1, 5, 10 per cent or more - you decide) to
cost-effective charities backed up with evidence will save lives and help to end global poverty. Resources will be less strained as well, as the lower the poverty rate, the lower the fertility rate. I link to GiveWell, which provides extremely detailed evaluations of charities and recommends top charities such as deworming charities which cure neglected tropical diseases, allowing children to go to school and get an education instead of suffering from these terrible diseases. Only a relatively small sum of can cure one person of such a disease.
There are reasons to think that this would be difficult in a capitalist system, though. There are no signs that the rich and powerful are prepared to abandon their free-market dogma. Moreover, what we know as capitalism is responsible for the continuation of the most serious existential threat to life on Earth, namely global warming. Global warming will
seriously hinder any effort to reduce poverty due to resources becoming more scarce, disease spreading, and so on.
So, we could abolish capitalism:
* If we abolished capitalism, there would likely be no currency. Without currency, society would operate on the principle of 'from each according to their ability, to each according to their need'. Essentially, the most vulnerable would get all the things they need, as would everyone else, of course. In our technologically advanced society, or certainly in the future, there may come a point where we can produce, with robotics, for instance, enough essentials to help everyone. In such a society, everyone would no longer be concerned about petty material goods and would instead be concerned about bettering themselves and humanity.
Sounds utopian, which is why this path is also difficult - the rich and powerful are unlikely to stand by and allow this scenario to happen either.
On world hunger, there is another way to help to solve it:
* A global move to a vegetarian diet would free up around 40% of the grain that we produce which is wasted when it is fed to fatten up nonhuman animals reared for meat. If this grain were instead consumed directly by humans, some estimate that around 1 billion more people could be fed.
But, certainly, on an individual level, voting for parties committed to policies that move away from neoliberal capitalist economics, giving some of your income to cost-effective charities and perhaps adopting a vegetarian diet are the things you can do to do your bit.