Assuming this adoption was done legally, and that it was in The U.S.,
than a new birth certificate would have been issued at time of the adoption.
If that is the case, than this person just has to request their birth certificate
the same way as anyone else, from the state vital records.
If they are trying to get their original birth certificate (pre-adoption and with
their original name) some states have passed laws that allow adoptees to
request the original birth record.
In The U.S. birth records (at least in the modern era) are held at the state level,
with the exception that New York City birth records are held only at the City level, and
birth records outside of the five boro's of NYC are held at the state level.
Many local towns/counties also hold birth records, and sometimes it may be faster to
obtain one from them rather than the state.
Where To Write For Vital Records
https://www.cdc.gov/nchs/w2w/index.htm
How to Find Adoption Records
https://www.usa.gov/replace-vital-documents#item-214647