Two of my sisters-in-law homeschool their kids, and this book outlines a large portion of their curriculum. I've looked for it at the library, but wasn't able to find it, but as luck would have it, my father-in-law had two copies, so I brought one home for myself.
I recommend reading it, and then supplementing your kids public school education by reading and then having them read the books listed.
I don't homeschool, but I've decided to implement this at home, nonetheless. The purpose is to teach our kids to be great thinkers and leaders. A lot of the time, the things they learn at school are just facts that are memorized and then regurgitated for a test. Or, they are trained how to do a job, but not how to think and form opinions.
So, I've started reading the books suggested, and I've had the girls read them too, in addition to their regular homework. They both love to read, so I've just asked them to alternate one of these books with a book of their choice in their recreational reading. We don't have formal discussions, but we talk about the books as we are driving in the car, etc. I've also started reading some of the books for younger kids to my boys, and they love it.