All states are different. Basically, though, one would need their curriculum signed off on. In the state I was in, a certified teacher could do that.
Curricula are available online, too. Good to use as a baseline. Goals are good to have as well. Set an educational goal you want your child to attain and find a curriculum that fits.
Biggest advantage of home schooling, AFAIAC, is that it doesn't need anywhere near the time to cover curricula as brick & mortar schools.
HSLDA is good to use as a trump card. There will be asshole school administrators trying to blow smoke up your ass. Know the law, stick to it, use HSLDA resources about the law for your state, and let them know your situation if there's a potential real issue. They don't really need to be called in. They're a big stick and having the school district know they're watching is often all you need.
In my cases, school administrators were so off base that the State Dept. of Education itself called them up and told them to get their shit straight.
Definitely have to know the law and follow it to a T. It's different for each state, but not difficult to get a handle on.