Adding media to a Page, Post, Gallery Media Post
Recommended Install the Simply Show IDs plugin (Via WP → Plugins → Add New) to display ID's next to Posts, Pages. By default Gallery Media displays ID's.
Attached Media Screencast
This screencast demonstrates using Attached Media and assigning it to a Stage Gallery.
Gallery Data Source - Attached Media
This allows you to add a Page/Post/Gallery Media Post ID (comma separated for multiple Pages/Posts). e.g. 306,178
The media must be attached to that Page/Post/Gallery Media Post ID otherwise the media will not show within the Gallery.
Locate Page / Post ID
To locate Page / Post ID - Edit your Page / Post and within the URL you locate the ID of that Page/Post. See diagram above. Alternatively install the Simply Show IDs plugin to display ID's next Pages / Posts.
There are two methods to attach media to a Page/Post.
Attached Media - Method 1
Goto the Page/Post and click the Upload/Insert Add Media (see icon above) button. Upload the images you want to be attached to that page. Once they're uploaded they become attached to that page.
Attached Media - Method 2
If you have already uploaded media - goto the WordPress Media page. Ensure you switch to the table view instead of grid to view attached media.
You can attach individual images by clicking Attach under the Attached to column.
Alternatively click the Unattached tab → Check (click select icon) for all the images you want to attach → Bulk Actions → Attach to a post → Apply → Search for your Page / Post → Click Select.