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 uses access to your space
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. See
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.
DO NOT CHANGE GROUP PERMISSIONS OR ANONYMOUS PERMISSIONS.
Restricting access to a page or portion of your site
(this is when things can get messy so proceed at your own risk.)