Birth records are considered vital records and are, therefore, accessible for free through the state they were issued in, according to The U.S. National Archives and Records Administration. If the state that issued the record is unknown, that information can be found via federal census records.
A list of state agencies that have access to vital records is found via the Center for Disease Control and Prevention at CDC.gov. The federal government does not release this information, but local state agencies have this information.
If this information can not be obtained, it is because these records were not recorded by local authorities; reasons for these exceptions are that the birth happened overseas, in Washington D.C., or because the birth happened within the military. The U.S. National Archives and Records Administration has additional resources to help someone seeking public birth records in unique situations, such as a birth occurring in one of the aforementioned exceptions, before vital records were kept, or if vital records were lost or damaged.
While birth records are able to be accessed for free, only certain people may obtain a certified copy of the birth certificate, and there is usually a cost involved as seen on the Pennsylvania Department of Health's website. Birth records are frequently accessible only after a significant amount of time has passed. This time varies per state but can be found by contacting the state agencies listed on CDC.gov.