This forum is for Javascript, not Java. There's a big difference.
And, regarding your question, you can use Javascript to see if Java is enabled. In case Javascript is disabled in a browser, then your checking would have to redirect to a separate page if both were enabled, and stay on the original page with whatever basic features you'd have if one or both were disabled.
One way to check if it's working is to simply try and use it. If you wanna see if it's working for a browser plugin goto a site that is using java. If you wanna check if you can run java programs, download and try to use a java program. If you wanna see if a compiler is working, compile a project you may have.
To that effect, here's a webpage with embedded java (aka java applet):
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