One of the questions I am frequently asked regarding homeschooling is "How do you know what to teach them?" It sounds like a simple question, but it really has alot of implications.
The question implies that, as a homeschooling parent, I am expected to teach my kids everything they are going to learn. In reality, they learn from lots of different people in multiple places. They attend various classes, events and lectures. They visit museums and science centers. They read. They watch various tv shows, movies, and documentaries. They learn from neighbors, friends, librarians, aunts, uncles, coaches and other kids and parents. As homeschool parents, Dennis and I view our role as the primary 'facilitators' to get them access to what they need and want to learn. I do not believe that I need to be able to teach them everything that they will ever learn (isn't that what youtube is for?!?), but to help them find the resources that enable them to learn. I also expect them to be able to find those resources for themselve in the coming years - just like Dennis and I when we want to acquire information.
This question may also mean how do I know when to teach them American History, introduce Algebra, study native americans or cover ocean life. There are many ways to accomplish this. There are many (probably thousands) of packaged curricula available that you could follow. Many are laid out comparably to how schools would cover those topics. We have used structured programs in the past. There is also a plethora of books that you could reference as to what your child might "need to know", if it were important to you to stay in step with children of similar ages that attend school.
We expose the boys to lots of people, places and things that prompt questions about and interest in Shakespeare, bees, geosolids, statistics, green anoles, pianos, trees, the human body, etc. and then get them books, activities, videos, websites, and museum exhibits about those topics. We find it is highly effective to teach them what they want to know, when they are actually interested. We are able to capitalize on their natural curiosity and interest in a subject. It is clear when they are done with a particular subject for the moment - and we move on the next!
One of the subjects people question how we will address is math. In our experience, the boys have been just as interested in math as anything else. We have not forced them to do specific lessons, and yet they have explored money, time, geometry, algebra, graphing, fractions, decimals, averages, addition, subtraction, mulitiplication and division, patterns, place value, the Pythagorean Theory, and much more. When they need to learn something we cannot teach them, we will help them find out where they can.