DFM is a product area and functions differently depending on if you are on the foundry side, developing a PDK for your customers, or the design side, incorporating the DFM checks provided by your foundry. Which side are you interested in?
In the documentation, some good starting points might be
- Examples using the DFM family of commands in the Calibre Solutions for Physical Verification manual (most of them are under "Advanced DRC")
- The user-specific chapters of the Calibre Litho-Friendly Design User's Manual
- (Requires separate download because it includes a design and supporting files to try out examples) Module 3 - DFM - of A Quick Start to Calibre Tools. Table 3-1 in that manual also lists the related training available for each DFM product.
Hope this helps-