My most favorite is a phone call from a third party or a letter. The reason for this is that it gives them a bit of space to react, think and absorb the information. No matter what method you choose, I highly recommend following up with a letter. DO research adoption laws in your state. Know what the statute says and know what you have access to, etc.
Most states have their statutes online, and can be located via one of the search engines.
Too much can go wrong and little is to be gained from this method. I know this from my own experience. When I searched for my birth mother, I took out an ad in the Dallas Morning News. Luckily my birth mother still wanted the reunion, but did tell me that she did not like how I went about it. I have seen MUCH worse happen to others using such methods.