Each state has its own constitution that runs the laws of the state that are not covered by the federal government. The 10th amendment to the US Constitution states that all powers not granted to the federal government are given to the states and the people.
Today, all the states governments are modeled after the federal government. They each have three branches of government including the Executive, Legislative, and Judicial Branches.
State and local governments handle a lot of the systems that we use and come into contact with on a daily basis. These include schools, police departments, fire departments, libraries, parks, and more.
Great Seal of the United States of America from the U.S. government
The head of the government in each state is the governor. Other parts of the executive branch may include the lieutenant governor, attorney general, and the secretary of state.
Just like with the federal government the states have legislatures that make up the state laws, handle the budget, and levy taxes. Every state but Nebraska has two houses similar to the federal government. This is called a bicameral legislature. Nebraska just has a single house.
Most State's Judicial Branch is similar to the Federal system where there is a State Supreme Court and then lower courts below them that handle the day-to-day cases.
Below the state government is the local government. There are even separate levels of government here. At the first level is the county government. Sometimes these are called boroughs or parishes. The next level is the city or town government. The powers and responsibilities between counties and cities can vary widely from state to state. In some states there is almost no county government, where in others the county is an important part and may be responsible for something as important as funding schools. Cities, or municipalities, often take care of things like police and fire departments, local courts, public transportation, streets, signs, and parks.
Local governments get their taxes in different ways to pay to run the government. Almost all states have a sales tax that adds to most purchases. This money goes to the local government to help pay for services. Most states have an income tax as well. Another major tax is property tax. If you own a home or a building or a piece of land, you will have to pay a property tax bill. This money generally helps pay for the school system, roads, and police/fire departments.