...in Linux

This is just about the easiest, at least for me. Two little common programs will accomplish a keymap switch in Linux: loadkeys dvorak (or loadkeys us to get back to QWERTY) from a console, and setxkbmap dvorak / us from within X.

As you probably will have a hard time finding all the letters for `setxkbmap us' when you're just learning Dvorak, it may help to put a couple of aliases in your .${SHELL}rc file:

alias aoeu='if [ $DISPLAY ]; then setxkbmap us; else loadkeys us; fi'
alias asdf='if [ $DISPLAY ]; then setxkbmap dvorak; else loadkeys dvorak; fi'

That way, you can switch back and forth just by hitting the first four keys on the home row.⁸

It's also easy to put the two layouts as menu items in X. In FVWM, it looks like this:

+ "dvorak" Exec exec setxkbmap dvorak &
+ "qwerty" Exec exec setxkbmap us &

This should immediately apply to everything. The only holdover I've ever seen is gaim, which likes to be restarted before taking the changes into effect. Hm, gtk ... ?