X2 to what has already been said...
Read what William says about the process HERE.
He pretty well sums it up.
I would add:
1. Unless you have some information about where the car was first sold, you going to have to trace back one owner at a time. So, did you get any info about ownership from where or whom you bought it?
2. When you write a previous owner or state DMV, if you just say you're looking for the original owner, then you will run right into privacy laws. I'd suggest you use phrases like "historic preservation" and say you're trying to ID the original dealership.
William is right. It's mostly a matter of luck unless you have a good lead.
I traced my 68 all the way back to the original owner and dealership for less than $10.00 and with just four letters: one to the state of origin, two to the previous owners, and one to the original dealership. I did start out well, because the guy I bought it from could tell me the original state. Along the way, I learned a lot about a previous restoration and got pictures from the original owner. The original dealership couldn't really help me that much because they didn't keep records that far back, but the sales manager gave me a boat load of info about the dealership back in the day.
In other words, no matter what the results, it's worth the effort. And who knows, you might get lucky!