Mac OS is great here because when you switch the layout, it immediately applies to all windows of all applications.
To switch, find the ``international'' control panel (pretty self-intuitive set of menus, similar in most versions of Mac OS), and click on the ``input'' tab. You probably only have the little US flag one selected (or just the one for whatever layout you use). There are two Dvorak options: plain old Dvorak (whose ``flag'' is a little black box with a `DV' in it), and what they call ``Dvorak-QWERTY'' (a little black box with a `DQ' in it). They both type Dvorak in all applications, but in the latter, QWERTY keys are used for the open-apple (command) keys. So, if you want to press apple-Q to quit an application, in Dvorak, it would look to an observer like you're pressing apple-X (the `x' key being in QWERTY where the `q' is in Dvorak); if you're using Dvorak-QWERTY, you will have to press the key that's labelled Q.
My friend Ben Schak says of the Dvoark-QWERTY option:
I'm a big fan of it, mainly because it makes all the undo, cut, copy, and paste commands stay next to each other in their familiar places. (I think the motions of those commands are more ingrained in my fingers' memory than the Qwerty keys ever were.)
When you select an option, a little menu comes into existence up at the top of your screen, displaying the flag of the layout you have selected. You can now switch layout by clicking on this menu and then selecting a different flag.
To make the menu go away again, open the International dialog back up and un-check all but one option.