Anyone with 2nd cousin matches at Family Tree DNA can try the Genetic Affairs automatic tree building to figure out which line they are related on – see how here https://blog.kittycooper.com/2020/03/automated-tree-building-with-genetic-affairs/. Otherwise use any combination or all of Genetic Affairs or GWorks or DNA2tree to find an ancestral couple to build down from. Then build the tree of ancestors back from a likely parent candidate and attach your DNA as his/her child. (Warning many of these 3rd party tools no longer work with Ancestry).
Read this summary of using DNA to find biological family at ISOGG – https://isogg.org/wiki/Utilizing_DNA_testing_to_break_through_adoption_roadblocks written by the DNA adoption people.
There is a wealth of material at DNAadoption.com whose objective is to teach you how to use DNA to find unknown parent(s). Thet have online classes on how to use DNA in your search. In addition, they have a google mailing list at https://groups.google.com/forum/#!forum/DNAAdoption/join (you must have a Gmail email address or at least a “Google Account”).
People who help adoptees with their quests are called Search Angels and they do not charge. There are several groups of Search Angels willing to help you out with your basic Adoption search including that mailing list from DNAadoption. Another group is the Soaring Angels on FaceBook – also there is this resource for finding a search angel which includes paid expedited searches – SearchAngels.org
The DNA Detectives Facebook page is a great resource for those with unknown parentage. They have over 50k members helping each other – https://www.facebook.com/groups/DNADetectives/
This article from Leah Larkin, the DNA geek is a terrific summery of the testing process:
There is now more than one book out on adoption searches: The Adoptee’s Guide to DNA Testing: How to Use Genetic Genealogy to Discover Your Long-Lost Family which is a good reference guide and more recently, available even on kindle, The DNA Guide for Adoptees: How to use genealogy and genetics to uncover your roots, connect with your biological family, and better understand your medical history.
Click here for my presentation on solving unknown parentage cases. Also I have a number of posts here on that topic. This is much easier for those with North American ancestry. I have a post which outlines the steps to use the DNAgedcom tools set called GWorks – http://blog.kittycooper.com/2017/09/solving-unknown-parentage-cases-with-dna/ which uses automation to compare the trees of your matches. Even easier, if you have an iPhone or iPad there is the DNA2Tree tool, an incredible app which works with your Ancestry.com results and finds common ancestors and builds their trees (click here for that post)!
These days, one of the clustering tools may give you a quick way to focus in on the lines to investigate, particularly if one parent is already known. Click here for my clustering posts.
Maurice Gleeson of Ireland regularly does talks about solving adoption cases with DNA, click here for his latest adoption talk on youtube. Click here for an older presentation of his with more details on these searches.
There are a number of stories about Adoptee successes on this blog at http://blog.kittycooper.com/tag/adoption-success-stories/