Best Searching Methods

Hi Everyone, I'm searching for information regarding my fathers birth parents. Both of whom are from New York. He was adopted by a family in California in 1955. Years ago he contacted someone who referred him to someone else (who he can't remember). They were able to provide names and information regarding his birth parents. Since then (years and years) that information has been lost. Without having to go through more private services and pay more money, what's the best way to find the names of his adoptive parents? I know his birth mother had looked for him years ago (this was discovered the first time my father received that initial information). So she wasn't hiding her name or anything. Doing google searches and such brings back countless websites that claim to do this and that, so hopefully some individuals on here have experience and can point me in the right direction. Thanks you! Scott