<p>How can I modify a SharePoint site so that versioning is turned on by default in Document Libraries?</p>

Versioning is not done at the site level, but at the list level.
If you want versioning to be turn on on each new library, you'll have to either:
Use your own library template (with versioning turned on)
Use feature + event handler to programmatically activate versioning on each new list
The easiest way is probably to use your own template. To do this, create a new document library, activate versioning, then save this list as template.
When you create a new list, you will then be able to use your template and directly create a list with versioning activated.