This application is best run in Mozilla Firefox. If it runs in anything else, that's a bonus. You may need to set your browser preferences to allow the right-click menu to be disabled: under Preferences, go to Content, then 'Advanced...' (next to 'Enable Javascript'), and ensure that 'Disable or replace context menus' is ticked.
Use a 3-button mouse to draw. Left button = black, middle button = grey, right button = white, or left/middle/right-click on the palette buttons to change.
To save an image, click 'Save' - this will fill up the text box with some hex data. Copy and paste this to somewhere safe. To load an image, paste some hex data into the text box and click 'Load'.
To use the Overlay feature, prepare a GIF/JPG/PNG image sized 512x384. Select this file in the 'Image file' selector, and tick the 'Enable overlay' box.
Opacity should be a number between 0 and 1, to determine how much the overlay shows through the graphics layer. After setting the opacity or selecting another file, click 'Load overlay'.
'Export' allows you to save this picture as a program to be loaded into a ZX81 emulator; when prompted to save a file, save it with the .P extension. (Thanks to Russell Marks for the full-screen display routine!)