In my site I have functionality for news and search results to show a pager to allow for pagination of the entries (like Google does, see screenshot). If I create a module for this, how do I call the module from within my .cfm template?

This can be done in many ways, but things that come to mind are a simple (cf)include, a displayModule or including a library like DataTables that does that automagically for you - just feed it data in the form of a JSON and never think of it again.