How to go about adopting a son who biologically isnt of u?

I have a son how is about to turn 4. His biological father is a deadbeat who wants nothing to do with him and has only seen him 1 time and only pays child support to stay out of jail. I have been with my husband for 3 years now and have been married for about 8 months. We have a daughter together. My husband is the only man my husband has known or has had in his life. My husband loves him and treats him as if he were ours. My son has my last name and we want to go about changing his last name to my husband but i dont know how. my husband also want to kinda adopt him as his own like as a guardian or something. How do i go about all this if its possible?