Locate the county you were adopted in and contact the county clerk. She will be able to tell you the process of seeking access to your sealed adoption records. There may be certain restrictions and varying orders of procedure--such as a rule that you must be of legal age to make the request on your own--but you will have to go to court no matter what, and the process for arranging that appointment is by filing a petition.
In all adoption searches, it is uncommon to find both the birth mother and father at the same time. A separate search, if desired, can be done afterwards for the father. Since males seldom change their surnames, and the mother might have additional information, it is usually easier than the initial search for the birth mother. In many cases, adoptees are able to do this second search for their birth father by themselves (or they try before paying for assistance).