<<I don't quite understand- how does an "unschooled" child learn basics- math, grammar, etc...?>>
Inspite of all our chatting about what unschooling is, I don't think any of us have answered your question! I will venture an answer, which can then be torn apart by the unschoolers on the board
Part of the premise of unschooling is that children will learn what is important to them when they find a need to learn it. For example, math is necessary for playing many games and doing many tasks, such as cooking or working with wood. As children find a need to use math, they will learn the math that they need.
Unschooled children can use text books as they, not their parents, see fit. So if an unschooled children finds it interesting or useful to work through a text book, they can.
The parent must trust that what the child really needs to learn, they will, and believe that we (the adults) do not know what will be most important for our kids to know.
I'm a middle of the roader -- we don't do school at home and neither are we unschoolers. Some ideas about unschooling that I find very easy to believe are:
1. The things that are considered basics come up so often and in so many ways that it would be difficult for a child with an active life and an involved parent to not learn them. That is why these things are considered basics.
2. Children learn things much more easily and quickly when they are learning for their own reasons rather than having someone else's time table and expectations put on them.
3. Grade levels, letter grades, and defined subjects do not add to the learning experience, and often get in the way. For example, elementrary school math is so redundant that kids can not do any formal math a year or two, and then catch up with their peers in a few months of concentrated work.