What are some tools for password protecting a staging site?

WordPress has an option to protect each page’s content using a password. That is done using the right panel just below/under the publish button.

However if you want to hide the entire site and make it visible only to users who are logged-in, then you should consider using a “maintenance plugin” or a “construction plugin”, you can look up for those terms in your Plugins section and try one of those plugins.