I am getting married in a few months and my fiancée wants to adopt my son. I have no idea who my sons biological dad is. So, how do I go about the adoption process.

There will be court rules on what you have to do to attempt a search for him, If he can not be found after an approved search, many states will allow for service though publication

Since this is a legal issue its been moved here from the Adoption forum. Start shopping around for a Family law attorney in your area. Every locale has their own rules about this. So you need a local attorney to prepare the paperwork. You will have to list all potential fathers and an attempt must be made, according to local law, to contact them.

But you need an attorney to do this to first tell you the requirements and then make sure the requirements are all met so a judge can approve the adoption.