The documentation was a little sparse so, if you’d like to subscribe to the click events on the tree nodes you need to add a selection handler.
This is how you add a selection handler to the whole tree:
Tree optionsTree = new Tree();
optionsTree.addSelectionHandler(new SelectionHandler()
{
@Override
public void onSelection(SelectionEvent event)
{
Window.alert(event.getSelectedItem().getText());
}
});



