I just want the fellow Airtable user to be able to use a base that I built as their own, populating it with data as they of their own, separate from mine. How do I do that?

After you create the “Read Only” share link described in the article @Elias_Gomez_Sainz linked above, when the other user opens that link to view your base, they will see an option to “Copy” your base into their own account. This copy they create will be separate from yours, and they can add/remove data without it affecting your base.