Teri, jumping in for Jan.
You get a rough idea if you see that someone has printed or reprinted your work. If it is printed, that means they went to the page that had a printer friendly version and printed it off for their own use.
If you see that you have one reprint, that means someone has clicked on the "Use Article for Free" link at the top (or what it is), and may have copied the plain text or HTML version of your article for use in a print or online publication. No guarantees. Sometimes people click on the link and don't do anything at all, but it will still be noted as a "reprint" or "print" when you look at the "Manage Your Articles" page.
If an article has been used in a print publication (church bulletin, magazine, etc), then you really aren't going to have much success tracking it down. If it is online, then you may eventually find it by doing a Google search for your name.
I've always given my work away because it's ministry first. But this is why members should only put things in the free reprint section that they are willing to have used without their knowledge. It can be helpful to do a Google on the titles of the articles from time to time as well. That may show it up as well.