From the Delaware Adoption Page:

How Does A Person Become An Adoptive Parent?

1. Gather as much information about adoption as
   possible, read articles and books, talk with
   adoptive families, attend Family Building Through
   Adoption course offered at Del Tech in Stanton.
2. Gather information about the licensed adoption
   agencies in Delaware and determine which agency best
   meets your needs. Only licensed adoption agencies
   can place children for adoption. The Office of Child
   Care Licensing, Division of Family Services, can
   provide information about agencies.
3. The licensed agency will invite you to come to
   an information meeting.
4. The licensed agency then invites you to begin
   the education and assessment process referred to as
   the home study. The process is an opportunity for
   you to determine if adoption is right for you and
   helps you consider the type of child you can best
   parent.
5. Home study processes vary from agency to agency.
   However, each must offer the following:
   • an opportunity for parents to explore their
     motivation for adopting, their strengths and
     weaknesses, and their parenting style
   • education about children that are currently
     available for adoption
   • personal and employment reference check
   • criminal history background check
   • review of physical and mental health history
     of all members in the home
   • home visits
   • physical and safety review of the home
6. Once you have an approved home study, the
   licensed agency will try and match you with a child
   to ensure that the child’s needs will be met.
7. When a child is matched and all parties believe
   that this child’s needs matches your strengths and
   abilities, a discussion of how to proceed with the
   placement should occur. It may be necessary for the
   child to visit initially with you so that
   familiarity and comfort increases before placement
   of the child into your home.
8. When all the involved parties feel confident
   that this is a good match, the child will be placed
   in your home.
9. If the placement involves a child from another
   state or country, contact will be made with the
   Office of Interstate Compact on Children, the
   Immigration and Naturalization Office or the State
   Department, as applicable.
10. The placement of the child will be supervised
    and supported by the licensed agency for a period of
    six months to one year, depending on the age of the
    child, as required by Delaware law.
11. Once the supervision period has passed and all
    parties involved feel confident that the adoption
    should occur, a petition will be filed in Family
    Court to finalize the adoption.
12. Children who are special needs may qualify for
    financial assistance after adoption. This will be
    determined before the adoption is finalized.
13. Information about post-adoption support groups,
    counseling, and other resources will be shared with
    you to support you and your new child.