With v2, dragging a document to another group or database moves it. Option-drag always makes a copy.
Another way to make a copy is to click-hold the proxy icon in the title bar (next to the document name) then drag the icon anywhere you want a copy. Always makes a copy if the move is inside DT.
If you need a copy of a document in the same group you’re working in, just click-hold the icon and drag it down to the group.
If you drag the proxy icon to the desktop it makes an alias to the original inside the DT database (be careful with this).
To copy a document to the desktop you still need click-hold option-drag the proxy icon.
A related navigation tip - if a document is open in a separate window, right click the title and see a list with an entry for each step in the path to that document. Click anything on the list and you’ll navigate to that point in the path.
(This is - sometimes - really cool in Safari for superfast navigating around a site.)
(Thanks to MacOSXHints for the clue.)