Mapping Center Answer:

So, this is a bit beyond the scope of just a simple question and answer exchange.  In some ways this is the meat and potatoes of GIS--the overlay commands in the toolbox are a good place to start--essentially, you're trying to winnow down set of areas to just the portions of each polygon that include what is relevant to you. 

In the basic sense of dasymetric analysis, the Union tool would be a simple way to start--If you Union your polygon data with polygon features that represent areas that you want excluded, then you have the basis for a query to select non-relevant areas from the Union result and delete them.

Also, in the dot density symbology, if you click on the Properties button (just above the Exclusion button) you can check on the option to "Use Masking", which performs a rudimentary dasymetric operation on the dot symbols by either restricting the dots to, or excluding the dots from the polygon dat you specify as the control layer.