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.

I have never seen, or heard of a program "app" that does this with a phone.
Posting the link may be the only way for a phone, but at least the F*BO sites imbed the video if the link is compatible.
If a person has a Google account they have to be carefull about removing the "s" (https://whatever when a link is posted or it may not embed in the page.