I do it similar to Brian. Unstring the bow and undo a few twists then insert the fur into the string and also a folded up piece of paper 'downstream' of the fur. (I normally put both fur strips in at this point) The I string the bow back up, wind the fur around the string and insert the tag end through where the paper is, then pull the folded up paper out. Then do the same for the other silencer, unstring the bow and twist the string back up.
Doing it that way ensures that the silencer is tight on the string. If it's wrapped loosely it can vibrate and give you a buzzing sound after the shot.