Why does the red-shift provide evidence to support both the big bang theory and the steady state thory?

1) as discovered by Edwin Hubble every distant galaxy appears to be moving away from us - and the further away it is the faster it is moving. This implies that a long time ago everything was closer together and even further back in history it must have all come from a single place.

2) the composition of the universe as measured many times over the past 50 years is roughly 75% Hydrogen and 24% helium along with 1% of the more interesting stuff (like planets and heavy elements) this is precisely what the big bang model predicts.

3) the Cosmic Microwave Background Radiation (CMBR) was discovered in the middle of last century - its a kind of afterglow in space from the big bang - and once again is precicely what would be expected to be seen.

As to how this supports the steady state theory... I suppose that would have to be wishful thinking on the part of the steady state theorists, because clearly it doesn't.