Our brick & mortar school days preceded our homeschooling days.
Basically, we switched to homeschooling when both public and private schools failed to work as well as we wanted. My eldest DD's methods of learning just don't mesh well with the typical classroom environment, and so we switched to homeschooling to end the seemingly endless battle we faced.
We were after-schooling in a fashion for several years before we made this switch, so we were anything but "hands-off". We didn't study extra subjects, but getting homework done required not only my prodding, but at times re-teaching the material the homework covered. At one point we asked for a second set of textbooks for certain subjects for eldest DD, so we could reference them at home without her having to pack 2 packs full of books to carry back and forth. I also volunteered on field trips and in the school library. I have found that for the most part the schools encouraged parent involvement, though we made it clear to them that we were seeking to work cooperatively with them, and not against them. When school teachings digressed from what we knew to be good science we taught our kids the difference (this was not always due to religious beliefs being included in the material, sometimes it was simply sloppy work on the part of the textbook publishers), but reinforced that they were to learn the stuff taught in school for school tests and discussions. We did not undermine teachers, though we did make use of the examples of how different people believe different things, and when it is appropriate to talk about the differences and when it is better to hold one's tongue.
Homeschooling, for us right now, is definitely better than the alternatives where we live. That doesn't mean it is perfect. This is only our second year homeschooling, and I am still working through several challenges myself. I expect this will be the norm until both kids are finished and in college.
One challenge is making sure the kids are challenged enough. When we made the switch we, of course, were switching curricula, and I ran my kids through the placement tests for the math curriculum I wanted to start with. I was surprised to see my youngest acing placement tests covering material she hadn't seen before (she figured out the logical way it seemed to go). I jumped her two grades in math, and could have jumped her 3 or 4, had I not been worried about missing some key element along the way that she would need later.
Presentation of material is another challenge, and a big factor in why the brick & mortar schools hadn't worked so well for us. Engagement is a constant battle, as is stubborn resistance to "boring" or difficult subjects. While I do present things in ways that don't work so well in a classroom setting I still keep in mind that I need to gradually train them to be able to handle college classes. These first two years I have concerned myself more with lessening the stress of school while getting information into their heads, but I am transitioning them into more analysis and more independence. They asked for more chances to work on their own; I just have to get on their case when they start getting lazy. I figure if I can get them to see how to find the engaging elements for themselves they will be able to stay on target when they hit college.
We use some organization that was learned in the brick & mortar school days, basically because we need some structure and this is familiar to us all. I use a weekly At-A-Glance planner, partly for planning out the next progression in some subjects, but mostly to record what we covered each day and what was assigned for the next day or week. By using a generic weekly planner I have the weekend days to note when we do things that relate to school, and I tend to include anything that affects our school schedule or day. I write down my own notes in this planner, but I also write a condensed sticky note summary of assignments to be worked on. The girls have their own preferred items they write the assignments down on -- I did not require them to do this, figuring I'd get to that habit later, but they like having their own checklist they get to mark up. Hooray, motivation for writing down assignments!
Another element learned from the B&M school times is I insist on Math being done in the morning. I let them try doing it later again recently, and this has only reinforced the need for Math in the morning. After lunch their brains just don't work as well on math, logic, or analytical subjects, and they tend to zone out and not listen as much. As a result our school days are structured something like my preferred schedule when I was in college: "classes" first, and reading and independent throughout the afternoon. In the kids' case this becomes math while Mom fixes breakfast, "class time" (any subject matter being studied that requires Mom's inclusion, with Mom instructing, answering questions, and assigning work to be completed) after breakfast, then independent work time, with permission always standing for either child to come get Mom if there's something puzzling or perplexing. Lunch usually happens right about the end of "class time", though sometimes not. Exercise workouts are part of class time, though Mom might insist on more impromptu ones if tempers are short, brains are fuzzy, or it's simply a gorgeous day outside.
I am a firm believer in the power and necessity of "recess" for ALL ages, provided it doesn't go on for too long at any go. Too long of a break, especially if it is too engaging, makes it difficult for any of us to get back to the work that must be done. However, when nerves are irritated, brains are foggy, or a golden day beckons it pays to take some time, 5 or 10 minutes at a whack, to get up, go outside, and just move about. If outside isn't an option just shaking things up with some silliness works almost as well. These brief changes of pace help a person (of any age) relax and let go of some tensions, which allows the brain to readdress the topics at hand with renewed clarity.
Looking forward I will have to transition to more and more rigor at some point, especially as eldest DD gets into high school. My state doesn't have rigid home school requirements (Texas). While this gives us a lot of leeway for figuring out how to do things it does leave me without guidance towards how to have my kids college- and work- and life- ready. I'm figuring this out as we go along right now, and trying to puzzle out what we should cover over the coming years from descriptions of other places' requirements, college entrance requirements, and quizzing my niece on what she is covering in high school.
At some point in the future I might try an online school for high school years. One thing my kids do miss is having classmates to visit with and study with, and a friend's daughter in another state has been doing online high school with some success. There is also one of those "iHighschools" here now, from what I've heard, which is like an online school that meets in person each week at the local community college -- my SIL is looking into the possibility of that for my nephew.