In the US, rules vary dramatically from state to state. Some states want full oversight, some practically require you to incorporate as a private school and others are very liberal and don't even care that you exist. In New Jersey, where we homeschool, it is very simple. Good overview here:
http://www.hslda.org/laws/default.asp

In general, grade school is not hard, once you brush up on your long division. High school can be more challenging just because you want to be able to document things well enough for college application purposes.

It’s not for everyone, and results may vary (just as with traditional schools) but it is certainly nice to have the option. Most of school is just learning how to learn.