How can my soon to be husband adopt my 4 month old son?

Is the father still living? He will have to formally give up his parental rights before your new husband can adopt your son.

Make a good faith attempt to locate the biological father and be prepared to present evidence of such attempt to the court. Then consult with an attorney who'll draft a motion to adopt. Once the motion is signed by you, your husband and the judge, the adoption is legal and binding. If you do manage to locate the biological father, he'll have to sign it as well.