Matt Ackeret passed along this tip for Apple IIGS: Dvorak is built in! Here's how to select it:
Matt didn't say what operating system software he was using. Also, I'm not sure about other Apple II models, except that the Apple IIc actually had a pushbutton switch next to the keyboard for switching to Dvorak.
For the Apple IIe, I have learned that one of the many jumper locations on its motherboard can be connected to turn on the vestigial Apple IIc-style Dvorak keymap. I don't know which jumper location does it, but I hear KeyTime (Tel: 206-522-TYPE) includes instructions for installing a switch with their Dvorak training package. Ask to make sure. (And if you try it, let me know if it works!)
Back to Introducing the Dvorak Keyboard.