School at Home
You might set up a class room. Follow the curriculum from your area or even buy one and follow it on line. You have work books and text book. The kids sit and read and write. You may even have a "school" room in the house.
This was what I did when I first started Home Educating, it isn't however what we do now!
Sometimes called Classical it starts with The Grammar Stage (6-10 years) where they learn the rules of language, memorise things, spelling, grammar, history, maths.
Then comes Dialectic (9-12 years) with discussion, debate and algebra, determining the why behind things.
The Rhetoric Stage (13-18) does "the systematic rigorous studies" and focusing on persuasive rhetorical arguments and ideas.
Un-schooling has it's own levels and depths but it is child-led. It is most often not sat at a table and un-schooled children tend to find education outside. They can do project based work, or no written work at all. The children set the pace and depth of the learning so it may be much deeper and at a higher (or lower) "grade". From physics to history and different cultures in an afternoon. This doesn't mean a parent won't organise a trip to a historic place or museum, or come up with ideas, it's that some the child will take what they find interesting and follow that. It can be truly terrifying to give that level of trust to a child but it works well for some people.
This British educator from the 1800-1900's method is about inspiring with great art and books. It has it's own curriculum but isn't forced on the child as it is presented as a buffet. It involves a lot of nature study, art and classical music.
Project based or Unit Studies
You take an idea (like Vikings) and everything is loosely based around that. There might be tablet weaving, or looking at why Viking boats were so good (by looking at the physics); the history, songs, foods (you can even eat those). You might write a poem like that of a Saga. You might look at their politics and the context of what was happening around the world at the time.
In some ways I do (and have done) all of these at different levels. When we first started I did school at home. Sat at a table and everything. We drifted more into units and projects which became more and more child-led. We would read very advanced (for her age) books and then discuss them and I took her to see art all over the country. We went on lots of nature walks and she studied the names (including the Latin) of the plants around us. We would watch documentaries and fall down interesting Youtube holes. We paint together. Make music together and the strangest thing can spark an interest.
We started learning an easy guitar song we randomly picked from Chordie. My daughter want to know more about the meaning of the song (The Cranberries Zombie) and she did a short burst of learning about the 1916 Irish Rising in Dublin.The whole thing lasted about 3 days but she learned to play the song well and has some context. She might dip back into it at some point, she might be done. We debate and question things we see together and have deep conversations about all kinds of things.
Sometimes I wobble and "make her do maths" because I suck at it and I worry about her not being able to do it. She is doing this well above my level (thank you Khan Academy). She has learned to "give it a go" and has tried all kinds of things from oysters to tae-kwan-do, to bush-craft, to cooking, to dog training, to painting, to Japanese, and blacksmithing, We have even looked at getting her an apprenticeship in blacksmithing.
When asked what she wants to be when she "grows up" she simply says "happy" which for some odd reason really confuses grown-ups!