It turns out that there is only one known pollinator - the yucca moth. These moths will fly around at night, gathering pollen from many flowers - they are very fragrant at night. When they are reproduce, they lay and egg in the stigma of the flower. Also, they seem to intentionally pollinate the flower, which will fruit and provide a food source for the developing moth. As the fruit matures, so does the moth, feeding off the seeds of the fruit. What it doesn't eat is left to grow into another yucca.
The page I found on hand pollinating yuccas, mimics the moth. Using a toothpick and a film canister, you collect pollen and insert it into the stigma, just like the moth. I practiced a little on my own flowering yucca, but without success. Before I had a chance at a serious attempt with the yuccas on my route, they were chopped down by the landscaping crew. Although I wasn't successful at it this time, I learned a lot about yuccas and their pollenation.