Examples of public finance are:
• Roosevelt's New Deal in which he ploughed public money and government spending into government projects to allow for more industry and, in turn, more jobs to be created. This helped the economy in the USA at the time as it got more people out of unemployment and into earning, meaning that there was increased public spending. Things like this are implemented with the current financial state of the country is in trouble.
• Tax rises and cuts are also examples of public finance methods, where the money that every working citizen must pay to be part of society is either lowered or increased, depending on the financial climate.
• Income distribution relates to the transferring of income from some groups to others. Examples of this could be public education, in which public money is ploughed into schools and teaching facilities, in order to create a better workforce for the country in the future. If natural disasters were to occur in the country, the people that are affected will be offered funding to get their lives back on track. It is basically offering money to the people that need it at certain times.
• There are also three different types of government expenditure: Government consumption, government investment and transfer payments.
There is a lot you can learn on public finance, so have a quick search on a search engine such as Google and read into the different aspects of public finance in your country.