How does the government raise money if they don't have enough money to pay for the programs allowed?

It depends on the level of government and the country you're dealing with. Most governments are primarily supported by taxes, so they may increase one or more tax rates in order to take in more money. The most common way of raising money to cover unexpected expenses, though, is issuing bonds--basically, the government asks for a loan from the people and offers to pay interest on the money it borrows. Individuals can choose to invest in these bonds (loan money to the government) and will later get their money back with interest.

EDIT: The U.S. Government often borrows from other countries in order to pay for various things.

ANOTHER EDIT: The US Government does not often borrow from other countries' governments. Individuals in other countries can buy US Savings Bonds just as US citizens can. In particular, a significant number of Chinese investors have bought large amounts of US bonds, so in that sense the US Government has borrowed from those individuals, but not from the Chinese government.