You can enable your stores private mode by:
Opening the store administrator
Navigating to the stores page
Edit the store you want to change
Select enable for the "mode"
Click "SUBMIT"
You as the administrator can add the customer to your store by:
Opening the store administrator
Navigating to the customers page
Clink the plus button (top right)
Select the store
Capture the customers email address (this is not case sensitive)
Click "SUBMIT"
A customer can request access by:
Opening your store
Signing in, if they have an account or signing up, if they don't
Clicking the "Request Access" button
Open the store administrator
Navigating to the customers page
Click the options ellipsis on the customer
Then click "Accept Customer" or "Reject Customer"