How does a statae, Indiana specifically, record it's population?

I really don't know other than the census. Maybe birth and death certificates Home ownership, taxes and other official records.

Im going out on a limb here "counting people"?

I think they can only estimate between census'es. I know that some tools they use may be, like others have said, birth and dealth certificates, and DMV records. If "Joe" moves from Glidesdale to Redrickstown, then his licence would show this when he got it changed.