Of all the emotional processes you go through when studying and researching your family tree it is the hunt for birth parents that is the most challenging. The locale privacy laws can make it a lot more complicated to find exact names and addresses depending on where you live. Even obtaining locations from the adoption agency or from your adoptive parents may be difficult. It is not uncommon that birth parents do not want to be found. You should be prepared for a long time spent searching as it can be difficult.
When starting out trying to locate your birth family ask your adoptive parents. You should understand they may feel rejected by this action. So you should try to be sensitive when approaching them for information. If you make it very clear that you wish to know your genealogy has nothing to do with them or the love they showed you as parents that will reassure them. Explain that finding your birth parents is in no way replacing your real family. Your mother and father may not to be able to give you any more than a first name for your birth mother. The adoption ageny could be the only thing they even knew anything about. Finding information from overseas adoption agencies is likely to make things a lot harder for you. If you are lucky you may find your adoptive parents had some meetings with your birth mother before the adoption. This doesn't mean they will know her name but any descriptive information about her age or some physical features may help you in your search.
Check out the laws surrounding adoption in your state and country. It may be worth your while to invest in professional help to assist with understanding the laws. Take care that you stick to the rules and always abide by the law. You may find some agencies who can help you and they are often to be found online. To assist in your search some legal advice will help a lot. Adoption reunions are worth looking into and you can usually sign up online. You never know, you may discover your birth mother is searching for you as well.
Eventually the agency that dealt with your adoption can be approached. They may or may not be able to help you but you should always ask. They may be prepared to pass on a letter you write to your birth mother. In your letter you would explain you want help to research your birth family tree. The adoption agency may also be able to tell you about your mother's medical records, if nothing else, so that you can be aware of your family's health history.
It may be tough but try not to simply give up when you hit problems. You may never locate your birth mother, but even finding out her name and age can help your draw up a family tree. Finding your birth mother is one thing but finding your birth father is likely to be much harder. If you are totally stuck, consider researching your adoptive family instead. It is, after all, their affection that was with you while they raised you and gave you their family name.