Subject: how do we detect expansion of spacetime?

If space were fixed and the universe was expanding, galaxies and such 
would appear to be receding from us. But I have read that spacetime itself 
is expanding -- if that is the case, our measuring devices (and everything 
else in fact) would be expanding at the same rate;  everything in the 
universe would countinue to appear to be at a fixed position relative to 
us.  (This is also related to the explanation for the big bang "leftover 
radiation" being uniform everywhere you look.)
The only way to see it would be to watch the expansion from 'outside'..  
I know that red shift is used to prove expansion, so maybe my question is 
more about how/why shift occurs.  The speed of light is fixed for all 
observers, why is the wavelength subject to shift effects due to observer 
motion?

Re: how do we detect expansion of spacetime?