Restricting editing or viewing to just certain people or groups is possible, but can get hairy very quickly. Unless your page (or site) has very specific security or confidentiality needs, it's best to keep things simple.
This instruction assumes you are the space admin.
Giving users access to your space - step by step guide
The default permissions for a new space are that anyone who is logged in to Confluence will be able to see (but not edit) content in your space.
Make sure the people who need access have Confluence accounts.
External collaborators must be invited to join Confluence - request an invite from the admins at Contact Us
Go to Space Tools (Cog in lower left of the screen)
Under Individual Users choose Edit Permissions
Search for the person by name
Add them to the list of users, and customize their permissions.
Typically, users should have permission to View All and Delete Own, as well as Add for Pages, Blog, Attachments, and Comments
If users need to be able to restrict access to specific pages, give them Restrictions add/delete
Best practices are to limit the number of uses with Admin privileges to any given space
DO NOT CHANGE ANONYMOUS PERMISSIONS.
ONLY CHANGE GROUP PERMISSIONS AT YOUR PERIL.
If you really, really, really, really, REALLY need your site to be available only to a small number of people, i.e., because you have sensitive content in your space (but not PII, because you don't ever put PII in Confluence)
Edit Permission for Groups and uncheck the boxes for confluence-users. Doing so will mean that no one except those explicitly listed in Individual Users will be able to view or edit any part of your space.
Restricting access to a page or portion of your site
this is when things can get messy so proceed at your own risk.
Each page can have view and edit restrictions that are more granular than the site as a whole.
Hover over the lock icon near the page title to see what restrictions are in place for that page.
To change restrictions, click on the lock icon or go to the ... in the upper right and choose Restrictions from the menu
To restrict editing only, choose Editing Restricted from the drop-down menu. If you are the sole editor, click Apply, otherwise search for additional users who need editing permissions, then hit Add and then Apply .
If you need to restrict both viewing and editing, choose Viewing and Editing Restrictions and proceed as above.
Once you place restrictions on a specific page every page below it in the hierarchy will inherit those restrictions.