First let's test if Java works. Goto http://java.com and click on this link "Do I have Java?" and Verify Java version. As you can see, Java plugin by default requires your permission to run, so it's disabled by default. But you may want to disable it permanently or remove your permission. Now I will show you how. I will select to always run Java on this site.
Now if you see something like this, then you have Java plugin enabled.
How to disable it?
Goto Customize -> Settings -> Show Advanced Settings -> Privacy -> Content settings ... -> Plug-ins
And there you can manage your permissions or you can disable plugins permanently. There choose to disable Java plugin.
Now go back into java.com and see if Java works and now you should see that no working Java was detected on your system, so you successfully disabled it.