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The red/ blue shift I think your talking about is the Doppler shift?
As objects receeds from us the light shifts towards the red end of the spectrum; the opposite happens for objects approaching us.
These shifts can easily be measured with a small scope and a simple spectroscope.
At the extreme, we have the Quasar's which appear to be receeding at close to the speed of light.
Maurice Gavin was the first amateur astronomer to measure the Redshift of a Quasar ( 3C273, mag 13). In 1998 he measured z=0.16.
There's not much a dedicated amateur can't do nowadays....
Hope this helps.
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