From Java applications, you can control the robot the same way. Your application should load the DLL and then the provided API will access the DLL using JNI. You need a different version of DLL: robotjava.dll. The documentation of the Java API is available here. Use the class robot.Robot to control robot from Java applications.
If you wish to write applets for controlling remote robots over Internet, you cannot use robotjava.dll - applets cannot use JNI. In that case, you can use the robot.RemoteRobot pure-Java implementation of the subset of the robot component (it is also documented). Also note that the standard Applet security will not allow you to control a robot that is listening for connections on a different machine than the server from where the applet is downloaded (in other words you will have to place your Applet on the virtuallab server - but we can assist you in doing so, if you like...)
Here is an example code for controlling robot from application: TestRobot.java, and from Applet: RemoteRobotApplet.java, for more, look in the cvs.