More specifically than color, scientists look at the wavelength of the main absorption peak of the star. To put it simply, molecules absorb and emit light at different wavelengths. There is not a single peak, but rather a series of peaks for each element. This is easiest to show through example. Take a look at the TOP chart here click please.

These are what the characteristic peaks look like for a primarily hydrogen star. See how they are evenly spaced? If we shifted the entire series of peaks to the right (red shift), the series would still look like hydrogen, just with the peaks in the wrong places. By knowing where hydrogen peaks without the red shift, we can compare the shifted peak locations to the unshifted locations to figure out how the star is moving. The shift moves up and down the spectrum, but doesn't change the shape of the peaks relative to each other.

Now, the BOTTOM chart at that link is for an older star, with less total hydrogen composition. Similarly, we see that it peaks most prominently in the green range. But, that hydrogen peak in the dark blue is in the same place. So, we have a reference point to tell if this star is red-shifted at all. (The graphs as presented are unshifted, so the peaks are predetermined to line up.

The bottom chart raises another question though, do green stars exist? The answer is yes and no. There are many stars that have peaks in the green area of the spectrum. However, they still emit large amounts of red, blue, and yellow light, and therefore appear white to us. The "flaw" in seeing them is in our eyes, not with with peaks! The sun is actually a "green" star, in that its emissions peak in the green area of the spectrum. Pretty cool!

Stars contain spectral lines that absorb or emit at a specific, known, wavelength, independent of temperature. If the light from the star is red-shifted, then the spectral lines will also be red-shifted, and since we know the wavelengths of the spectral lines, we can know how big the redshift is (in fact, this is how we measure redshift). Knowing the redshift allows us to reconstruct the star's original spectrum, and from that, its original temperature.

This said, if a star is far enough away that we would notice a significant redshift, it is probably too far away for us to see it directly, i.e. we can see the galaxy that the star is in, but won't be able to pick out the star itself from its neighbors.