Summarize:

It's the app with an icon that looks like a blue compass. Type https://www.java.com/en/download/installed.jsp in the address bar and press ⏎ Return. It's a red button in the center of the page. This may prompt a pop-up window asking if you want to run Java on this page. The website will detect what version of Java you are running and recommend an update if needed.
Open the Safari browser on your Mac. Go to https://www.java.com/en/download/installed.jsp in Safari. Click Verify Java Version. Click Run, to confirm.