If you coil your rope in circular loops, you actually introduce a half twist in the rope for every loop. This can make the rope difficult to manage. While it can be avoided by giving the rope a half twist for each coil, it is easier just to "butterfly" the coils.
Butterflying means to alternate the direction that you loop the coils to avoid introducing a twist. You end up with a pile of coils on each side of your hand, like a pair of butterfly wings.
See the pictures at right for more details. Notice the way that in the bottom two pictures, the coils hang on either side of my hand. Continue doing this to the end of the rope, and then secure the loose end.
If you have a long rope, you can shorten the process by starting with both ends in your hand, and doubling the rope. It certainly reduces the strain in the arm holding the coils.
You can also download an animated GIF (360kb) that plays the images at right in an animation.
If you find your arm still gets tired coiling long ropes, have a look at coiling over your neck for an easy method that saves holding the rope.