How should I go about making an Adoption application?

You should engage a Lawyer to prepare all relevant documents and file a Originating Summons (Adoption) in the prescribed format. Some of the documents which will be filed together with the petition are:-

(1) an affidavit verifying the contents of the Originating Summons,
(2) the child’s birth certificate,
(3) the marriage certificate of the adoptive parents if the Originating Summons is jointly made by the spouses,
(4) the consent of the natural parent(s) or guardian(s),
(5) the consent of the other spouse if one of them is the applicant.