I teach my kids at home. I happen to be very qualified. I have a Bachelor of Science in Education although I do not hold a teacher's certificate. (I forgot to send something in and didn't get it 20 years ago. Now I would have to take new classes every year to get one.) I have a master's. I have a PhD. I have over nine years of teaching experience. In addition to that I have taught part-time and taught my kids for the last seven years.
What does it take to be qualified to homeschool?
Some states have specific regulations. You have to have more education than your child. You have to have a certain number of hours of college. You have to be a college graduate. You have to be a certified teacher.
Some states don't.
I'd say the first thing it takes is the desire to homeschool. If you don't want to do it, for some compelling reason, then don't. If you do want to and you have a high school eduation, then you shouldn't have any trouble. If you want to and you don't have a high school eduation, you may have to work harder at it when your child gets to high school or find another alternative then. (Private school, an academic program somewhere, dual enrollment at the local community college.)
I'd like to say the second thing you need is patience, but I am not sure I have that, so I don't think I can require it. I do suggest it though. It will be easier for you and your children if you are patient. If not, you'll learn it, but it will more difficult for everyone. (Been through that one.)
Then, of course, you need to find out what your state requires and prepare for that. Do what they require.
For coursework, you can go a lot of different routes. I have. You can go to the local teacher supply store and get curriculum. (It will be very expensive because it is intended for classroom duplication and you will need it for only one or two children, but it can be very good.) You can go to a hotel meeting in the summer and look at A Beka books. They are also on the net and will send you a catalog. Ditto with Bob Jones Press. (They're associated with Bob Jones University.) You can find your local homeschooling group and go to the book fairs. The big publishers come to those and so do people trying to sell old books. You can get copies of the public school curriculum. I don't recommend that, but I do know people do it.
Then you have to find what works for you. It may take a while, but it can be done.