How do I draw in an off-screen image?

After you've created the offscreen image, you can draw into it by getting the appropriate Graphics object, which you get by calling getGraphics on the offscreen image. Here's a basic example:

Canvas c = new Canvas();
Image i = c.createImage(10, 10); // create offscreen image
Graphics g = i.getGraphics();
g.drawRect(0,1,2,3); // draw into the offscreen image