Please help: procedures for adoption of illegitimate child

I have an illegitimate son, and has been abandon by his father, his not consistent with his financial support his based on hongkong and I don't have any idea where exactly he is now, right before he abandon us, he said that He is not the father of my son though he had sign on my son's birth certificate, he said why don't we just separate and said that if my sin will look for him I will simply say that he's just a friend of mine, so I decided to go on different way, now I am married with the man who I think is very responsible and he wants to adopt my son, how can we do that what are the exact step by step ptocedure and how much will it cost us?

Or if ever

How can I ask for his support for my son?
What are the procedures? His mother is here in the Philippines I also tried to ask for their financial support but they insist, that it's out if their concern only his son can decide, and added that they are willing to support my son only if my son will be on their costudy and I don't want it to happend. Please do help me please.