How do I make a rug out of excess carpet

you would need to put a binding on the raw edges of the carpet piece.

Cut to shape and add Carpet Binding or have a Carpet Co. Whip the edges for you, or Sew a Fringe on........

If it is worth it for you to spend a little money, call a company that sells carpet and see if they have they can edge it for you.

http://funcheaporfree.com/2012/03/savvy-saturday-projects-make-your-own/

You will have to bind the edges somehow...perhaps with an iron on fusion tape and seam binding...(the pile of the carpet may have to be trimmed back in order to get good adherence

Sometimes if you ask the store where you got it, they will bind it for you - maybe for nominal fee.

Every scrap I've ever used had a binding added by a carpet company... You've paid for the expensive part (the carpet), let them do the rest... It'll even Look right!