This is a complex problem with many solutions. Many disagree and possible solutions are always controversial. Here are a few areas that get a lot of discussion.
Many who live in poverty do so because they never received quality training or education. It is often difficult for untrained workers to find lucrative work. Because of this, children of the poor are less likely to get good educational opportunities as well. This can create a cycle of poverty. If governments or non-government organizations can provide better education in poorer communities, it can help end the cycle of poverty.
Many people live in poverty in part because the society where they live is in some way biased against them. For example, in the United States, people of color have historically combated prejudice and discriminatory laws that make it more difficult to escape poor circumstances. Some of these issues continue today. A possible solution is to promote awareness and government policies that help reduce discrimination and institutionalized racism.
Often poverty is the result of economic downturn. If there are no jobs in the area, many will live in poverty. This problem can be solved by promoting business in the community and encouraging policies that help promote hiring and expansion. By creating jobs, more people will be able to work and more people will be lifted out of poverty. The tactics behind this are complicated. Some think it is best to lower interest rates or taxes. Some think it's better to invest in technological research. The idea is to encourage commerce that will lead to higher employment.
These are only three of many, many proposed solutions to issues of poverty. There are many opinions on the issue.