To move page families, you require 'Create Pages' permission for each page in that family. Space Permissions are assigned by a space administrator from the Space Administration screens.
To move an entire family of pages from one space to another, or within a space
Go to the top most page (parent page) in that family.
Click on the 'Edit' tab. The page's current location is listed below the title input-field.
Click 'Edit' beside 'Location'.
From the drop-down menu displayed, select the space to which you want to move the page family.
If you want to specify a parent page, click on the Choose a Page icon and select the page from one of the tabs displayed. Or else, use the search facility to locate the page.
If you want to move the page directly under the new space, leave this field blank. See Working with Page Families for more information.