Gather your information about the process and then tell everyone you know that you want to adopt. You should also consider putting together a profile. A profile is many things and sometimes it is as simple as a from the heart letter to the birth parent(s), other profiles contain pictures, family backgrounds, educational and work histories, etc. There is no magic formula for any profile and often when speaking with birth parents about the couple they choose they say something just clicked when they read that particular profile.
Some adoptive parents go through agencies where they pay a flat fee for the adoption. Many agencies have long lists of adoptive parent(s) waiting for babies. With an agency adoption the adoptive parents often are not aware of the baby until after the birth parents have signed the relinquishments. Some agencies are however participating in open adoptions where the natural parents review profiles of adoptive parents and sometimes there is a meeting between the couples.
A private adoption is one where an agency is not used and the adoptive parent(s) and the birth parent(s) come together by a number of means. Sometimes attorneys have birth parents looking for adoptive couples and sometimes attorneys have profiles on hand of adoptive parent(s) looking to adopt. Some people meet through the Internet and others are brought together because they happened to mention the idea to a friend who knew somebody who wanted to place a child for adoption.
While there is no legal requirement that adoptive parents have legal counsel, in private adoptions, both the adoptive and birth parent(s) should have competent legal counsel to assist them in the adoption process. In some counties in the State the Court will not take a birth parent consent or relinquishment unless they have legal counsel to represent them.