Very little.

Not much is actually known about Pythagoras himself. We know that he lived in Greek southern Italy in the 6th century BCE, and that he established a group of followers whose philosophy impacted later Greek thinkers such as Plato. However, the evidence linking various mathematical discoveries to him and his school is weak. The two mathematical results most often attributed to him are Pythagoras's Theorem and the incommensurability of the side and diagonal of a square. Both, however, were likely known in Mesopotamia before Pythagoras, while their earliest proofs appear well after him and sources attributing the results to him are late and unreliable.

A fair amount of trigonometry was codified a couple of hundred years after Pythagoras in Euclid's Elements, though in a geometric rather than trigonometric fashion. The title 'father of trigonometry' is usually given to Hipparchus of Nicaea, who lived in the 2nd century BCE and compiled some of the first trigonometric tables. The modern trigonometric functions sine and cosine, however, actually derive from 6th century Indian astronomy, via translation to Arabic and then to Latin. Hipparchus (and later Ptolemy) used the circle-based chord function instead.

Postscript: One mathematical result more plausibly credited to the Pythagoreans is the relation of musical harmony and physical ratios. Furthermore, Aristotle credits Pythagoreans with the theory that "things themselves are numbers", which is interpreted by some as an early claim that mathematics can be used to describe reality.