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You can either do this before attempting to save the video to your "Watch Later" list or clicking the "SIGN IN" button on the pop-up dialog that appears after clicking the "SAVE" button.  If you're not signed in, you may be prompted to sign in before continuing. In that case, do so and then click "SAVE" once redirected to the video page after signing in.  To access the "Watch Later" playlist, click the ≡ hamburger menu (triple line) at the top left of the webpage and select "Watch Later" from the list.
Sign in to YouTube. Navigate to the video you wish to save for later. Click "SAVE" underneath the video. Check the box next to "Watch Later". Finished.