I suggest that first you work with clustering techniques, for instances, kmeans algorithm, one of the easiest and fastest to compute and then try with dbscan or a agglomerative technique since there is not a technique better than other, depends on the data. Follow CRISP-DM methodology or KDD process since the preprocessing phase is very important to obtain meaningful clusters.  A good book to learn about clustering is Data Mining: Concepts and Techniques, Second Edition (The Morgan Kaufmann Series in Data Management Systems) by Jiawei Han

First of all, you have to define the properties you are interested in. Is it age, gender, city? Or you want to group together the customers accordingly to some more tricky properties such as average balance, monthly income etc? Then you have to realize how to obtain such properties for each customer. You want a simple 2D table with customers in rows and their properties in columns. After that you can use e.g. some clustering technique as Marta said.

Clustering. However due to categorical attributes involved they need to be represented in quantities of numerals for similarity or proximity measures. The best way would be to use them as priori information and cluster numerals then associate them in rules.

Good luck