There are several different technical measures of residential segregation and a long technical literature on the development of these measures. For an overview, see, http://www.census.gov/hhes/www/housing/resseg/app_b.html. I draw from this for the brief notes below.
Massey and Denton used an extensive literature search and cluster analysis to identify 20 different indexes of segregation and classify them into five key dimensions of segregation.[1] Basically, evenness involves the differential distribution of the subject population, exposure measures potential contact, concentration refers to the relative amount of physical space occupied, centralization indicates the degree to which a group is located near the center of an urban area, and clustering measures the degree to which minority group members live disproportionately in contiguous areas.
The two most common indices of segregation you will encounter are the index of dissimilarity and the isolation index.
Conceptually, dissimilarity measures the percentage of a group's population that would have to change residence for each neighborhood to have the same percentage of that group as the metropolitan area overall. The index ranges from 0.0 (complete integration, no-one would have to move) to 1.0 (complete segregation, 100% of a minority group would have to move)
The isolation index measures "the extent to which minority members are exposed only to one another," (Massey and Denton, p. 288) and is computed as the minority-weighted average of the minority proportion in each area. Another way of saying this, is how likely is an individual to encounter a co-ethnic in their immediate space (in our example, it would be for census tracts).
For segregation measures based on census data from 1980 to 2000 for the Boston MA-NH PMSA, see:
http://mumford1.dyndns.org/cen2000/WholePop/WPSegdata/1120msa.htm
For segregation measures based on census data from 1980 to 2000 for the Springfield MSA, see:
http://mumford1.dyndns.org/cen2000/WholePop/WPSegdata/8000msa.htm
[1] Douglas Massey and Nancy Denton. 1988. “The Dimensions of Residential Segregation” Social Forces 67:281-315.