The sums are very straightforward. There are two calculations you can do; one is non-relativistic and the other is relativistic. The relativistic is obviously what counts for red shift. Browse around for a link that suits you, sir.

I don't have any problem with the calculations; the problem I have is understanding why the equation should be z = delta lambda / lambda for a Doppler shift. I guess I'll just have to work on it.

Doppler's effect:

λ' = λSqrt[(1+v/c)/(1-v/c)]

where v is the star's receding speed with respect to us. So:

Δλ = λ'-λ = λ{Sqrt[(1+v/c)/(1-v/c)] - 1}

so Δλ depends on λ and if you measured the red shift with Δλ you wouldn't have a unique value, given a unique value of star's distance D. In the Hubble law, it's Δλ/λ which is related with that parameter:

Δλ/λ = H*D/c

http://en.wikipedia.org/wiki/Redshiftsince, for little v/c, {Sqrt[(1+v/c)/(1-v/c)] - 1} ~ v/c, you also have:

Δλ/λ ~ v/c --> v/c ~ H*D/c -->

v = H*D.