To start, make a slip knot.
Reach through the loop, grab the long end of the rope, and pull it through to create a new loop.
Reac through the new loop, grab the long end of the rope, and pull it through into a loop. Lather, rinse, repeat, until you get nearly to the end of the rope. At the very end, grab the long end of the rope and pull the whole thing through the last loop.
To undo this, you just pull the final end of the rope out of the loop, and yank on it. Voila! The whole thing comes loose.
In my photos, the ropes are all doubled over and then doubled over again before I start. The first time you try this you should do it with a single strand of rope, but once you get a feel for it (which should be very quickly), it will all make sense and you can double the ropes over first.
If you'd prefer an illustration, here is one from a crocheting how-to page; look for the basic chain stitch. Note that they're using a crochet hook rather than hands to grab the yarn, since the loops are much smaller.