Specifically, download and install
Java. If you have Java installed already, it may not have associated .jnlp files properly. Use "Open with..." and browse to where you have java installed and find "javaws.exe" (should be in something like c:\Program Files\Java\jre1.8.0_66\bin).
If you're still having issues, you may need to allow Java to run in the web browser. Open the Java control panel. In the "Security" tab, make sure "Enable Java content in the browser" is checked. While there, make sure to add the two domain names the game uses to the exceptions--"http://game.havenandhearth.com" and "http://www.havenandhearth.com"
Opinions expressed in this statement are the authors alone and in no way reflect on the game development values of the actual developers.