Decide on the purpose of the research. The research's question must be one of how certain groups are similar and whether you can predict group membership through individual characteristics. For example;
How do men and women differ? How do tenants in the city differ from those in the suburbs? Are those living in rural areas more likely to move into the city or suburbs upon relocation? Are all suitable questions to investigate through discriminant analysis. Your analysis need not be limited to two groups, though limiting your analysis this way makes the discriminant analysis algorithm more objective and less complex.
Decide on the variables of interest. These are the variables on which you expect the two groups to differ. For example, if you are researching the differences between tenants in suburbs and the city, your variables of interest might be ones such as "salary," "ethnic group" and "age."
Randomly sample from the population of interest, collecting data on the variables of interest. In researching the differences between city tenants and suburban tenants, collect data by randomly sampling from databases of tenants in these two areas.
Find the centroids of these groups. Enter the data into a statistical software package to calculate the centroid of each group separately. Keep a record of these centroids.
Randomly sample from a new population -- one in which the classifications are unknown or not included in the original classifications. Sample on the same set of variables that you used for the previous sample. For the example of researching suburban dwellers and city dwellers, you can sample those living in rural areas in hope to understand whether they are more likely to relocate to cities or the suburbs.
Classify each data point in the new sample according to which centroid they are closest to. See if the results are of statistical interest and can answer the original question.