Depending on where you are the world, your rights and responsibilities as a home educator will differ. In some countries such as Germany and Greece, home-schooling is illegal. So the first thing you need to do, is establish whether the country you reside allows home education or not. (you may find this chart listing the legality of home schooling in different countries helpful).
Home Schooling in the UK
Since I'm in the UK, my focus will be on the legal rights and responsibilities of a home educator here. This post is not at all professional legal advice, rather just information I've come to understand and learn from my own experience as a home schooler over the years.
Just to note, if you're reading from across the big pond over in America, then know that each State has their own laws and regulations. You can read more about your State and homeschooling here.
Alhamdulillah we're blessed in the UK in that we can indeed choose to educate our families at home, and the law gives us the freedom to teach our children without specifying any particular curriculum, program or learning philosophy. You do not have to follow the National Curriculum.
There is a well known phrase which goes around the homeschool world:
"Education is compulsory, schooling is not."