A gray area should appear to the right here with buttons, a grid, and blue pentominoes. If you are only seeing a blank rectangular area to the right, then try clicking in that space. This has worked in some browser/Java combinations.
Try to place the pieces in the box with no overlapping. There are many ways to do it.
Check here for more detailed instructions, source code, and the development stages of this applet, i.e. how this applet was built, step by step.
This applet, version j, runs under compilers supporting Java 1.1, unless there's a problem with the compiler. If you get an error on the Java console like "pentominoes class not found" then it's probably because you have an older JRE (Java Runtime Environment). Version g of this applet should work in that case. Check here to see how to check your Java compiler version.
For your convenience, here are all the sites I can find that have OOG v1.2: