How does Hubble Law relate distance to velocity?
They are proportional, at least for nearby objects.
Originally Hubble discovered for the near galaxies that the further they are, the quicker they are receding from us.
His law was this:
Here v is the velocity, H is the Hubble-constans, and d is the distance. The velocity is calculated from the redshift by Doppler-effect, the distance with Cepheidas and the Hubble-constant is what you measure for real.
Later they discovered that this is not the correct way, beacuse it's not the galaxies what are receding from us, but the space itself between us and the galaxy is expanding, and that causes the redshift. Also, on long enough distances, the Hubble law is not entirely proportional. By taking these two into account, you can understand the past of the expansion and predict the future of it. That's how they discovered the accelerating expansion of the Universe, and the dark energy what causes it.