Well Michael, if you lived just one town over and had been in my ninth grade World History class in Montclair, New Jersey, then you would have been there when Mrs. Whatshername showed us the film Little Buddha, which taught me both the story of how Sakyamuni founded Buddhism, and how Lama, the priests of Tibetan Buddhism, seek out tulku, or reincarnations of past Lamas or other holy figures.
This is how Ask Yahoo (sorry, Ask Yahoo!) explains it.
In Tibetan tradition, the Dalai Lama is not only the spiritual and secular leader of Tibet, he’s the reincarnation of the Tibetan patron deity, Chenrezig, the Buddha of Compassion. Today’s Dalai Lama, Tenzin Gyatso, is the 14th reincarnation.
Like the rest of the Dalai Lamas, Tenzin Gyatso was put through a series of tests as a small child before he was officially declared the reincarnation, or tulku, of his immediate predecessor. His Holiness was enthroned as the Dalai Lama in 1950, but has been leading his followers in exile since 1959, when the Tibetan resistance to Chinese occupation collapsed.
In recent years, the Dalai Lama has discussed the possibility of the Tibetan people ending the tulku tradition, and the belief that his own reincarnation will not happen in Tibet while it remains under Chinese control. That leaves some uncertainty as to where and how the next Dalai Lama will arise, and who it will be. If you think it could be you, it might pay to have faith. It worked for Steven Seagal.
Of course, you could always say that the next Dalai Lama will be the current one. After all, it’s the same spirit, right?