If you were adopted, then you know how frustrating it can be not to know much about your heritage and genetics. Finding your birth parents can help you learn more about your family history and where you came from, as well as answer any questions you might have as to why you were given up for adoption and if you have any other biological family members.
Talk to your adoptive parents about any information they have about your birth parents. So they don't feel threatened by giving you information about your biological parents, be sure to tell them that you love them but are curious to find your biological family. Ask for names, an old address, the adoption agency or anything else they might know about your birth parents.
Go to Ancestry.com or a similar website to look up your birth parents' names and see if you can find census records, birth records or marriage records. You can sign up for a free trial with the website and purchase a subscription if you find it helpful in your search.
Contact the hospital where you were born for your birth records. While it is not done routinely, you could explain your situation and, at the very least, get a name and an old address to track down your birth parents. An old address can lead you to a neighbor who might know where your birth parents went or have forwarding information.
Seek out the adoption agency that you were placed with. It should have information as to whether your biological parents wanted you to contact them, and it might have the contact information so that you can find them. The agency may also have information if your birth parents never wanted to be contacted by you.
Register with the International Soundex Reunion Registry. This puts your name on the registry so that your birth parents can find you as well as you finding them. You can also search the database to see if your birth parents registered.
Finding your biological parents may take many attempts. If you really want to find them, don't give up your search. Make sure that the parents that raised you feel loved and appreciated for what they've done for you.
Finding your biological parents may not have the fairy tale ending you are hoping for. Be prepared to meet regular people, with regular lives and regular problems.