Using Sidebars

This is a pretty rudimentary question, but I suppose I find the documentation vague on creating a page with a custom sidebar.  When I create a custom sidebar and add the desired widgets, how do I then specify to use that sidebar when creating the page?  On the Page Attributes section, I select (No Parent) under the Parent section, but when I choose “Right Sidebar” under the Template category, it gives me your predefined sidebar with numerous widgets I don’t want.  I would have expected to see the sidebar that I created and named show up under this drop down list as an option.  I followed the documentation as shown and there is obviously something missing???