How old is Saruman?

Sauron is a one of the Ainur, which are comparable to gods or angels. The Ainur exist in two groups: the Valar and the Maiar. The Maiar are lesser beings than the Valar and serve them.

Sauron is a Maiar, and so he has existed since the very beginning of Ea (the world). To make a guess based on the chronology of events in Tolkien's world, Sauron is at least ten thousand years old.