How does one add a new base field to a content entity?
Adding fields just works. Define the new field, run update.php, it will compare the new and existing definitions and figure out that there's a new field to create.

Renaming/deleting fields works too, but only when you have no data. When you have data, then you will still need to write an update hook, or a migration. We're missing documentation on how that will look exactly, but basically, you use the same schema functions as in 7.x and then update the last installed field definitions.