The laws of the state in which the child was adopted determine who has access to the original birth certificate or other adoption records, and whether those records are sealed (unavailable). For information about the law in each of the 50 states and the District of Columbia, see the: http://www.childwelfare.gov/adoption/. This links to the Child Welfare Information League’s numerous publications on the legal aspects of adoption.
When my wife and I adopted our son, we were told that we needed to hire multiple attorneys. One to represent the birth mother. One to represent the child. One to represent the birth father. And one to represent us. When we adopted our daughter we needed even more. One for the child. One for the birth mother. One for us. And one for each of the three possible birth fathers! We were outnumbered! Since no agency was involved, the attorney fees, the home study and the court costs were our only expenses. And when it came time to file our income taxes we claimed the adoption tax credit and were reimbursed the entire amount. Both times. We were fortunate. Adoptions can be, and in most cases are much more expensive.