While the child's mother may retain parental rights, she does not have custody. If the child is in foster care, the bio mom does NOT have a say over where the child resides even temporarily and it is too late (from my understanding) to do a private adoption. You would do well to contact an attorney who specializes in adoptions. You might want to do this sooner rather than later.
A homestudy involves having a caseworker from an adoption agency, or your state dept. of child welfare, interview you and your spouse, along with the members of your family living in your home. You will have to have a criminal history check, including an FBI check, along with some sort of home safety inspection (they're looking for fire extinguishers, smoke alarms, etc.), and tons of paperwork regarding why you want to adopt, what your philosophy of parenting is, etc.
Hope you find the info you need with the lawyer.
Hopefully it will be straightforward with few hoops to jump through.