Buddhas continue to live on through their teachings as dharma bodies. Their spirits become manifest in the sangha (spiritual community) where their teachings are passed on.
Nirvana means to extinguish the burning fires of the Three Poisons: greed, anger, and ignorance. This can be accomplished by letting go of dissatisfaction.
Examine the present and learn from the past to see how the future will unfold. Too often we just look at the present and base our actions solely on that.