If you are looking for biological parents/childen given up for adoption, here are the most logical first steps in a search:

1. Talk to your adoptive parents. Get as much information about your adoption from them as you can.
2. Contact the adoption agency used. Ask if a letter has been left for you by your birthparent(s). Ask to leave a letter with the adoption agency containing your contact information in case your birth parents are searching for you.
3. Contact the courthouse in the county where you were adopted. Ask if your birthparents have left information for you with your birth certificate/adoption papers. Ask if you can leave a letter with your contact information with that information. Please note that not all counties will do this, and even if they do, they may have different rules on how you go about it.
4. Register on reunion websites. Adoption.org, adoption.com, and ISRR are 3 of my favorites.

There are also many adoption search sites with Adoption Search Angels that will help individual find their medical history information and enable contact if possible.
These groups are located all over the internet. And Search Angels dedicate their time and expertise to helping people along their own journey.