There are many different types of homeschool education. You need to find the type that works best for your family and matches your student's learning style.
These are the main subjects taught in homeschool education, no matter which type of education style you choose.
I will probably add more in the future. Right now, we're homeschooling kindergarten.
I could write pages on each of these topics, and I may at some point, but here are the absolute basics that I consider most important:
Personally, I am a fan of Waldorf and Reggio Emilia, probably because I am an artistic person. Doing crafts gets me excited and makes me a more passionate teacher, but if you don't like crafts, find a different style that works for you.
I was worried that I might have off days when I can't concentrate enough to do spelling and math, so I wanted a scripted program for those subjects that tells me exactly what to say and do.
The ideal homeschool education style also really depends on your student, especially as they get older and have more input on how they learn best. Some kids can be handed a stack of workbooks, go through them alone, and do great, but others need a more hands on approach and interaction.
I highly recommend you study personality types as described in The Child Whisperer to better understand your child and yourself.
The word origin of educate means to lead out or draw forth.
I believe that the purpose of education and raising children is to help them find their purpose and passion. They need to discover their life mission for themselves. We can guide, but they already have something inside them that must be discovered and drawn forth.
The opposite viewpoint is that children are sponges or empty vessels to be filled. I agree that they pick up on things in their environment, but they are absolutely not a blank slate to write on as you please!
People choose to homeschool or use public school for different reasons, but we all have the same destination in mind: a healthy, competent adult.