Some states allow lesbian and gay couples to adopt children jointly, making both parents legal parents at the same time. Usually, these adoptions are done through domestic or international adoption agencies or independently (where the adopting parents deal directly with the birth parents or through an intermediary, like an attorney).
Another way to become legal parents is for one lesbian partner to give birth to the child and the other partner to adopt the child, either through a second parent or stepparent adoption. (To learn about second parent and stepparent adoptions, see Nolo's article Types of Adoption.) Gay male couples can do this too, by using a surrogate to carry a child born from one partner's sperm and a donor egg.
Some states specifically bar gay and lesbian couples from joint and second parent adoptions. To learn more about the legal landscape of same-sex couple adoption, see Nolo's article Gay and Lesbian Adoption and Parenting.