To use the "my favs" section, do the following:
Look for a video you want to save and click the star or bookmark icon.
Proceed to any video you select and click the bookmark icon shaded in gray and once you select it, it will change to black. (Note, if it is already black, the video is already saved)
Now, simply click the "my favs" icon (star or bookmark) on the app menu bar and you will see your saved news!
To remove a video from your "my favs" page, simply click the star or bookmark icon until it is grayed out. It will be removed from the "my favs" list automatically.