Who survies the flood, and how is the new race born?

Which specific flood are you referring to?

If you're referring to the Greek Flood, Deucalion and his wife Pyrrha are the only survivors. Deucalion was the son of Prometheus, so when Zeus sent the flood, his father warned him to prepare beforehand. And after the flood, the way they restore humanity is to toss stones over their shoulders after consulting an oracle. The stones that Deucalion tossed became men and the ones that Pyrrha tossed became women.