Some typical data mining techniques:
Segmentation / Clustering - Using a stats package such as SPSS or SAS to cluster data into similar groups (normally the groups are groups of customers). Pioneered by Tesco's / Don Humby in the 90s, the famous example was when Tesco segmented their clubcard customers into different groups and analysed what they were spending their money on. They realised that their "mother and baby" group weren't spending enough on baby products (as they didn't trust cheapo Tescos for stuff for their babies) so were shopping at places like Boots instead for their baby stuff. Tesco's spent a lot of money marketing to these customers to convince them that their baby stuff was OK and managed to steal a lot of custom from Boots.
The most common clustering technique is K-Means which is popular as it can handle processing large chunks of data. There is probably a technical explanation of how it works on wikipedia (something to do with establishing centroids and then sending each data point to it's nearest centroid).
Decision Trees / CHAID / CART - This is a way of linking independent variables to a dependant variable (similar to regression models) and works by running lots of t-tests. The output will then give you a tree diagram that shows which of the independent variables is the biggest predictor on the value of the dependant variable (and also what the natural cut-off is for the independent variable in question). An example application of this would be spotting users who are likely default on loan re-payments. You would feed in independent variables such as number of payments missed, age of customer etc and then the resultant model would "score" each of your customers on how likely they are to default (so the model would be established on a known group of older customers that you already know whether they default or not and then applied to a newer group of customers to decide which are in the high-risk category).
Linear Regression / Binary Regression - Similar to decision trees (linking independent variables to a dependant variables) but works by running "least square regression" tests for all of the variables rather than t-tests. The application and output are almost identical to decision trees (linear regresion is when you are predicting a scale variable such as "value of customer" and the binary version is when the dependant variable is a yes/no, eg "will customer default on loan?"
