@Kadybug18,
Your first stop is your mother (if she is alive and will cooperate with you). Ask her for everything she remembers, pictures, where and how they met, etc.
You may not hear nice things. She could be angry about him being absent. He could be dead, married, homeless, committed to an institution, or in prison.
If she is not helpful (or willing to help) or is no longer among the living, try her siblings, her parents if they're still alive, and anyone you knew who worked or went to school with her at the time, or even a neighbor from that time.
You are looking for a location before almost anything else. This will help you to narrow down if you've got the right Mike Smith (or whatever his name happens to be). It will also give you more of a jumping off point for finding data like birth and death records.
You may not find anything. As I mentioned before, you may not like what you find.
But above it all, I do hope you'll tell your mother that you're grateful that she raised you, okay? The subject of your father is probably a rather difficult one for her. You can make it easier by giving her props for being there when he wasn't.