Easiest IMO to remember two things. First is to exchange when you're ahead (you already know this). Just be sure to remember that some pawnless endgames are a draw even when you're a piece up (and some are a win but very difficult).
So
So basically go ahead and exchange when ahead... but the defender is happy to remove all the pawns.
If you want a 1000 caveats, start a discussion thread. 
Good stuff Irontiger, John, Yaro, Samky, ZBorg and also all who contributed on the previous page.
I appreciate your time and helpful contributions.
(If there is anyone I forgot to thank who contributed, then thank you too.)
One idea which I haven't heard expressed yet is that the value of the rare pawn(s) left in the endgame lies in their capacity to promote to Queen, thus hugely affecting the power balance, and also in their threat to promote to Queen, which usually means that after the 6th rank it becomes increasingly likely that one's opponent is going to be obliged to trade a piece to kill the pawn. So one advantage of the extra pawn is that it can be used to capture more material - passively by being exchanged by the opponent's minor pieces to prevent promotion; and actively by Queen capturing loose pieces in simultaneous attack.
All of which goes to say that things are a LOT more complicated than 15 rules in the back of Basic Chess Endings.
Please pardon one last comment? Fine comments that one needs to be ahead at least a Rook in material in order to mate. Good general rule to think of when joyfully swapping pieces off the board: do I have enough of an advantage to win? And: since there are exceptions to this rule (e.g. "someone usually gets the better deal in every exchange" and blocked positions cripple bishops, etc) we can't just weigh the material balance of a future exchange and know we can win. Thank you for your patience with a rookie.
Thank you Irontiger. Finally the right answer to learningthemoves question.
In my post #12 I wrote, "...If you would like to know the common sense reasoning behind the principles when you exchange pawns and when you exchange pieces please let me know..."