If the star and galaxy spectra (on the left) are cross-correlated the resulting function is shown on the right (solid line) -- it is an offset peak with finite width; the offset gives the redshift and the width of the peak gives the velocity dispersion. If the star is cross correlated with itself (i.e. its autocorrelation) you get the faint dotted peak on the right. It is the difference in the width of these two peaks that gives the stellar velocity dispersion.
Recall: cross-correlation is the function arising from summing the cross-multiplying of two spectra, and repeating as the spectra are shifted relative to each other.
Cross correlation peaks for the Mg triplet and Ca triplet regions (shown on the left).