There are a few ways, the easiest being just exchanging names. Then when you walk up to the podium you each give the other person's name.
With the double booking rule, this only works for an even trade.
If the original ADR holder needs to cancel the ressie so they can make another one elsewhere, then call Disney and tell them that they are giving the ADR to their "friend, they give the name and party info of the other person to the reservationist (find out which resort they are staying at). Then as a courtesy I like to PM the confirmation # to my new friend!