You contact an adoption agency or a social worker licensed to do homestudies. Costs will vary state to state and agency to agency - we paid $3k for ours over 10 years ago, but I know other people who used other providers who paid less about the same time and still others who paid much more. It does not necessarily help to shop around - our agency would only take homestudies done by them, and they were the only agency in our state who had access to Korea as a choice. Pick your agency or method of adoption first (you may work through a lawyer or do a private adoption without an agency in many states), then do the homestudy that they need.
A homestudy will likely involve one or more home visits, perhaps writing an essay about yourself, getting references, probably a background check on you and everyone in your home, perhaps a workshop, probably getting a letter from your doctor.