I had a puppet like this a long time ago named "Cowboy Carl" I believe his line ran from the wrist (like stiqman said) to his ear.
Interestingly enough, he also came with rods.... it was somewhat self defeating as the fishing line limited the range of motion of the arms with the rods attached... I ended up removing the fishing line

I'm totally digging up an old thread here and blowing the dust off it.... but it was something that caught my eye and I just had to respond with my own little two cents.
When I attend (or used to anyway) conventions to display & sell my puppets from a booth I would have all of their arms suspended by the fishing line method, but I also provided arm rods too. I attached one end of the fishing line to the ear or under the chin (if there wasn't ears) and then the other end had a loop on the end of it to wrap around the three fingers (not the tumb) of the puppets hands..... this made the fishing line optional. If someone wanted to use the arm rod then all they had to do was pull the hand out of the fishing line loop. Since the fishing line is transparant, no one saw it when it wasn't in use but it was always there if the performer wanted it.
-Michele