There are many ways that parents can choose to homeschool their children.  Below are some widely known methods.  It is by no means a complete list, but rather a jumping off point for you to begin your research to find what fits your family. 

Charlotte Mason Method

This approach advocates reading good books from original sources and spending lots of time in nature. www.simplycharlottemason.com

Classical Education

Many Christian and other families prefer a liberal arts education for their children, including lessons in Greek and Latin, as well as formal instruction in logic. www.welltrainedmind.com

Distance Learning

Companies and schools that provide teaching assistance as well as learning materials. These schools vary widely in their choice of method, let alone formality.

Eclectic Homeschooling

Some like to pick and choose among various methods, enjoying the flexibility it affords.

Montessori

Maria Montessori advocates observing your child, removing obstacles to learning and providing children with real, scaled-to-size tools to use. http://www.montessori.edu/homeschooling

Thomas Jefferson Education

Jefferson hypothesized that literacy and self-government work hand in hand and was a key component to self-preservation. There are many websites about this method, just do a search.

Umbrella Schools

Independent Study Programs, Distance Learning Programs, Virtual or Cyber Schools, Charter Schools, Learning Centers.

Unit Studies

Available free or for sale to homeschoolers. Also instructions on how to make your own are available on internet and in books. There are many unit studies that you can find free on the internet.

Unschooling

Natural learning is letting your child lead the way. www.unschooling.com