Many novice homeschoolers or those with not entirely supportive spouses will begin with traditional homeschooling. This method is essentially school at home. Traditional homeschooling relies on textbooks, workbooks and methods virtually identical to regular public schools.
The classical method focuses on grammar, logic and rhetoric. This method often includes the study of Greek and Latin and heavily emphasizes memorization and language arts skills. It is basically a liberal arts education. (See references 4 and 1.)
Charlotte Mason advocated instilling a love of learning in children, thus academic sit-down lessons take no more than an hour or so a day. The rest of the time is spent in natural learning activities like reading real literature, going out into nature and keeping a nature notebook and doing dictation exercises.
The Montessori method of education stresses the learning environment and unstructured teaching. By providing children with the right tools and encouragement, learning takes place naturally. Outside of prepping the environment, the learning that takes place is largely student-led. (See references 1, 3 and 4.)
Unschooling isn't exactly what it sounds like. Education definitely takes place—in an unstructured and child-led way. Unschoolers let children study things as they show interest in them. For instance, a child has a fascination with weather. His parents will go to the library and bookstore and bring home an armload of books on the topic. They will go online and find weather experiments for the child to try. They may go as a family to visit a meteorologist as a mini-field trip. Parents can work in most school subjects using their child's interest. Math can be used to convert Celsius to Fahrenheit. The student can do language arts work by writing a paper on the worst tornadoes in U.S. history.
Unit studies are theme studies. For instance, a unit study could be on transportation, or about the French Revolution, or insects. Once the theme is set, books are gathered. These can be nonfiction or fiction. Activities based on the theme are worked into the study. Field trips, Internet studies, projects and essays are all worked around the theme. Almost every subject can be tied into any theme. By working in a unified manner, unit study enthusiasts contend that students comprehend and retain the information better.
Eclectic homeschoolers look at education as a buffet and pick and choose from the different methods and apply them as best fits their family's educational needs.