Homeschool laws vary from state to state. The best thing to do when you are interested in homeschooling is to do some research on your state's requirements. A good place to start is http://www.hslda.org/. This is the website for the Home School Legal Defense Association and they list the requirements for each state.
Where we live (Arkansas) we have only a few requirements. We are required to fill out a Notice of Intent to Home school and file it with our school board every year. On this form we do have to list what kind of curriculum we will be using and how many hours per day/days per week/weeks per year we will be homeschooling. We also have to sign a form stating that the state is not responsible for our child's education. Our only other requirement is that children in grades 3-9 are required to take a Standardized Test (Iowa Tests) once a year. This is not done in a public school, but instead at a testing site set up and monitored by homeschoolers. This year we were only required to take Math and Reading so the testing is only one day for 3 hours. In the past we have had to test for several days when the full battery of tests were required. Our nearest testing facility is 40 miles away so I am glad we only had to test one day and very grateful that my friend was able to take Chelsea today.