There are a few different ways to homeschool. Depending on your personality, your approach to your homeschooling curriculum will be different. Some might favour a more flexible syllabus while others may prefer a more structured program.
The Home Education Association (HEA) conducted a survey and noted the diversity of homeschooling methods and curriculum choices among families. They found the different approaches chosen by parents included:
15% families unschooled. 31% preferred natural learning methods. 8% adopted a school at home approach. 11% used the Charlotte Mason approach. 8% used the classical approach 27% were eclectic homeschoolers. 
Unschooling is education through daily experiences. If a child expresses interest in learning something, parents can facilitate that learning. For instance, they could go shopping and learn about mathematics and business. Learning happens as a part of their family life. Unschooling was coined by John Holt. Holt said unschooling should allow children as much freedom as the parents can bear so they can learn.
Natural Learning or Radical Unschooling
Natural Learning (or Radical Unschooling) is when children are encouraged to follow their interests completely and whole-heartedly. Parents give children the freedom to learn what they like. This is also called radical unschooling. They let their children make all the decisions - no chores, no rules, no bedtime, no exams and no meal times. They don't tell children what to eat, or when to go to bed or how much television or video games they can watch. Some claim radical unschooling is unparenting because parents, in the words of Lorraine Devon Wilke, seem to 'abdicate their role of parents'. Radical Unschooling is about as 'free' as 'education' gets.
Charlotte Mason Approach
The Charlotte Mason Approach was founded by the British educator, Charlotte Mason. Mason thought that basic reading, writing and arithmetic skills should be taught to homeschoolers. Apart from those subjects, all other learning should be conducted by exposing children to other sources of knowledge. This method exposes children to real-life situations and gives them plenty of time to play and create. They show adults what they've learned through dance, art and writing.
The Classical Approach focuses learning on grammar, logic and rhetoric. While the early years are spent absorbing facts, the middle-aged student starts thinking critically through the arguments they learned in their primary years. The high school student learns more about how to express themselves. The Classic Approach focuses more on reading and writing and accomplishes learning through written and spoken works rather than TV, videos and pictures.
The Eclectic Approach uses ideas from other homeschooling syllabuses to make its curriculum. Eclectic learning can include attending school part-time, doing distance education and/or e-learning. It tends to get information from multiple sources, styles and theories to gain a complementary understanding of a subject.
References:  Parliametary Enquiry Final Report into Homeschooling. Published 5 December 2014.  Sandra Dodd, 'Definitions of Unschooling' <http://sandradodd.com/unschool/definition.html>. This is a pro-radical unschooling website. Also see 'Extreme Parenting 'Radical Unschooling' ABC News' (2010), ABC News on Youtube, <https://www.youtube.com/watch?v=2aQf2FjdxbQ>. Georgina Dickson 'I Let My Children Do Whatever They Want' (2012) Gulf News, <http://gulfnews.com/life-style/i-let-my-children-do-whatever-they-want-1.1108729#.ULGP4cOEWTI.facebook>.  'The Unschooling Movement: Good Parenting or UNparenting?'