When I first started searching for my own birthparents I attended an Adoptee's Liberty Movement(Alma) meeting and received the following tips for searching. First obtain a copy of your Final Adoption decree from either the adopted parents, state, or county courthouse. If your parents are dead, the court will send it to you with no problem as long as you send them death certificates. The reason they will send it to you then is the parents were the clients of the agency. With them dead, they are no longer clients, therefore you are entitled to the records. Write for your Non-Identifying information from either the state, county, or agency that handled the adoption. You are entitled to it.
Later check school yearbooks. Check probate/civil indexes and records. Check birth summaries. Also check newspapers' Vital Statistics. Ask the adoption agency for Court of Jurisdiction. If you get a name check Polk City Directories as residents of a city are listed in the front by Surname. It will give the wife's name, occupation and address. The back of the book lists streets in alphabetical order. Check old phone books. Libraries have them on microfish. Check marriage records as they will like the brides maiden name. Marriage application lists age at last birthday. Check death and divorce records. Signing up for Ancestory. com is helpful but expensive. Since I was foundling I had a very hard time searching but did find information in the end. Check out my book, Finding Me in a Paper Bag: Searching for Both Sides Now which is for sale on Ebay.
Check out my guide of searching do's and don'ts. Good luck.