When it is on server side, use web services - maybe RESTful with JSON.
When Java code is in applet you can use JavaScript bridge. The bridge between the Java and JavaScript programming languages, known informally as LiveConnect, is implemented in Java plugin. Formerly Mozilla-specific LiveConnect functionality, such as the ability to call static Java methods, instantiate new Java objects and reference third-party packages from JavaScript, is now available in all browsers.
Below is example from documentation. Look at methodReturningString.
Java code:
public class MethodInvocation extends Applet {
public void noArgMethod() { ... }
public void someMethod(String arg) { ... }
public void someMethod(int arg) { ... }
public int methodReturningInt() { return 5; }
public String methodReturningString() { return "Hello"; }
public OtherClass methodReturningObject() { return new OtherClass(); }
}
public class OtherClass {
public void anotherMethod();
}
Web page and JavaScript code:
<applet id="app"
archive="examples.jar"
code="MethodInvocation" ...>
</applet>
<script language="javascript">
app.noArgMethod();
app.someMethod("Hello");
app.someMethod(5);
var five = app.methodReturningInt();
var hello = app.methodReturningString();
app.methodReturningObject().anotherMethod();
</script>