Downloading Youtube video

This question relates to my phone (Samsung Note 3) how do you copy a playable youtube vid ( ya know the one with the arrow in the center that you simply click to play) I have been unable to do that and post in this forum or send in a message. Whenever I try to copy a vid all I get is a link to the vid. I do not have a youtube account and don't know if that is the reason. I have never had a problem viewing one.