You can upload photos/videos by tapping the Add button in the bottom-right corner of the Album tab or Recents tab. Then select the items you'd like to upload.
Grandparents and other relatives can upload if an Album Admin (parent member) has turned on "Allow Album Member Uploads" in the Settings tab.
With Premium Family or Premium Family Pro, you also have the option of uploading photos and videos from your computer.
For more information on uploading from your computer, please see the following article.
How do I upload from my computer?